Tootfinder

I have just submitted a grant application to the Swedish Science Council with the title "Functional multi-objective optimization under uncertainty".
https://patrikja.owlstown.net/posts/3782
If granted it would pay for a PhD student supervision time.
Some prelimina…

Nous lançons une campagne où chaque objectif Š atteindre correspond Š une facture juridique afin de collecter des fonds pour couvrir nos frais d'avocat dans l'affaire OKC-Spatz en cours d'instruction en France.
Soutenez-nous pour que la justice soit rendue. #JusticePourLesVictimes
1/2

Now in Kleine spoel at @… "Free Software - it's more than coding" by Birgit Hücking.
#tdose

I consider these kinds of events to be nearly useless symbolism, preaching to the choir.
I do accept that these events are useful as means to meet others, but one should not expect these events to have even the slightest impact on the maga/white-nationalist/musk-ites... Nor do I think they have much impact on those who are in "the middle" and do not particularly engage in politics.
"Nearly 1,000 gather at Main Beach to create ‘Resist!’ human banner protesting Trum…

Nearly 1,000 gather at Main Beach to create ‘Resist!’ human banner protesting Trump administration
Around 1,000 people gathered Saturday morning at Santa Cruz Main Beach to spell out the word “Resist!” The event, organized by Indivisible Santa Cruz County, aimed to protest the Trump administration and celebrate Santa Cruz Pride’s 50th anniversary.

Kammerdämmer

NaaS – No-as-a-Service
No-as-a-Service (NaaS) is a simple API that returns a random rejection reason. Use it when you need a realistic excuse, a fun “no,” or want to simulate being turned down in style.
– from @…
❌

GitHub - hotheadhacker/no-as-a-service: No-as-a-Service (NaaS) is a simple API that returns a random rejection reason. Use it when you need a realistic excuse, a fun “no,” or want to simulate being turned down in style.
No-as-a-Service (NaaS) is a simple API that returns a random rejection reason. Use it when you need a realistic excuse, a fun “no,” or want to simulate being turned down in style. - hotheadhacker/n...

physics_collab: Multilayer physicist collaborations (2015)
Two multiplex networks of coauthorships among the Pierre Auger Collaboration of physicists (2010-2012) and among researchers who have posted preprints on arXiv.org (all papers up to May 2014). Layers represent different categories of publication, and an edge's weight indicates the number of reports written by the authors. These layers are one-mode projections from the underlying author-paper bipartite network.
This n…

Maybe I'm reading too much into this, but the top looks like Homer Simpson and the bottom looks like my mother accusing me of doing something I didn't even do.

A very funny piece...
Puccini – Gianni Schicchi
https://www.youtube.com/watch?v=CaT7V14A2vo

OK, so here is purportedly ICE doing a raid ... and the news media quietly accepts, from "agents" who displayed no proof that they were actually Federal agents, much less their identity.
How can we know that these masked men (most of 'em are men) are actually who they claim to be?

ICE arrests several workers from South Park restaurant
U.S. Immigration and Customs Enforcement agents made arrests Friday afternoon at Buona Forchetta, an Italian restaurant in the South Park neighborhood of San Diego.

physics_collab: Multilayer physicist collaborations (2015)
Two multiplex networks of coauthorships among the Pierre Auger Collaboration of physicists (2010-2012) and among researchers who have posted preprints on arXiv.org (all papers up to May 2014). Layers represent different categories of publication, and an edge's weight indicates the number of reports written by the authors. These layers are one-mode projections from the underlying author-paper bipartite network.
This n…

I'm supervising a group of six 3rd year BSc students in a project inspired by the paper "Responsibility Under Uncertainty: Which Climate Decisions Matter Most?" https://link.springer.com/article/10.1007/s10666-022-09867-w
The project description is availa…

It's been 7 months since the D-party lost the easiest-to-win election the US has ever had. And it's been 4 months since FFOTUS took office and became a modern Caligula.
And what has the D-party done?
Nada. Nada. Nada. The old faction is spinning in useless circles defending Biden's inexcusable decision to continue to run until too late. The younger element still shows no sign of engaging in the voting part of politics. Our middle-age element still looks first at t…

Eben erst war Hilde mit dem Abstauben der Friese, Simse und Putten hinten fertig geworden. #SchiffSamstag

Yesterday my schedule and the weather suited a return to gliding for the first time since the fires. I did four flights - the second was a checkout in a new type (the Grob 103), and the third a little soaring trip in the Schweizer 1-26. The first and fourth were just commuting in the Cessna 172.
#aviation #gliding

What a glorious morning! Still not sure how I feel being awake this early on a Saturday, but definitely happy to be heading in for #SotB2025 (and then #GoldfishLive later!)
Gonna be a fun day 😁

This https://arxiv.org/abs/2503.16393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity $=$ Volume formula and Newton non-degenerate ideals in regular local rings
We develop the notions of Newton non-degenerate (NND) ideals and Newton polyhedra for regular local rings. These concepts were first defined in the context of complex analysis. We show that the characterization of NND ideals via their integral closures known in the analytical setting extends to regular local rings. We use the limiting body $\mathcal{C}(\mathcal{I})$ associated to a graded family $\mathcal{I}$ of ideals to provide a new understanding of the celebrated "Multiplicity $=$ Volume" f…

Willkommen, auch (aber nicht nur) im #prideMonth! 🏳️‍⚧️🏳️‍🌈
Handgemalter #wandklexschmuck, alles zu finden hier:
#fediArt #mastoArt #creativeToots #miniaturepainting #artjewellery

Malta – Marsaxlokk – Triq Il Wilga
#kamafotos

Sleepy garden cat is unimpressed with your human shenanigans #Caturday #CatsOfMastodon

Ist das da rechts nun nicht
Das Alarmanlagenlicht?

Hey gang - if any of you are going to be in DC and attending the FFOTUS imperial march on June 14.
Remember, try to gather, early (so you get into the front row) across from the viewing stand (which will probably be on the south end of the white house lawn).
I recommend that when FFOTUS appears that you give him a full Braveheart mooning.
You can wear underwear - and I suggest that on the left side it has the letters "T A" and on the right "C O".
I…

Landgenoten en mede-aardbewoners, was het niet heerlijk om in de rode mensenmassa te lopen gisteren?
#rodelijn
The people
United
Will Never Be Defeated

Three months after the fires, I finally took a break from work, disaster management, and re-establishing domestic infrastructure. I flew up the Owens Valley to Lone Pine, and and spent last weekend walking in the desert, biking in the foothills, and gazing at the stars.
#aviation #California

Checked in at Yugo Restaurant. Sashimi lunch for me, house bento for Rachael. This place is great!

[2025-05-30 Fri (UTC), no new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

Malta – Marsaxlokk – Triq Il Wilga
#kamafotos

I hadn't planned on migrating several sites away from Netlify over the bank holiday weekend, but nevertheless, here we are. They didn't leave me much choice...
https://theadhocracy.co.uk/wrote/buh-bye-netlify

Kussrot knospts im Morgenblau
Schlafweich und voller Regentau.

Interesting piece, especially when taken in conjunction with FFOTUS' crazy tariff wars.
"How America Lost Control of the Seas"
Of course, as with many things that have gone wrong in the US, it begins with Ronnie Reagan.
https://www.theatlantic.…

How America Lost Control of the Seas
Thanks to decades of misguided policy choices, the U.S. has an astonishing lack of maritime capacity.

The 80th edition of De Programmatica Ipsum is out!
This month, we deplore the sad state of the Windows operating system; in the Library section, we review “The Old New Thing” by Raymond Chen; and in our Vidéothèque section, we learn about how the Longhorn project derailed through Dave Plummer.
https://…

And another #bootdotdev certificate! #golang

I noticed yesterday that if you call Wells Fargo that their announcement now says "Your call may be recorded *or analyzed*"
Oh, and Wells also added that fake typing sound to their awful call-tree. What, do they think that we believe we are talking to a real person who is typing at a keyboard?

This https://arxiv.org/abs/2503.16393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity $=$ Volume formula and Newton non-degenerate ideals in regular local rings
We develop the notions of Newton non-degenerate (NND) ideals and Newton polyhedra for regular local rings. These concepts were first defined in the context of complex analysis. We show that the characterization of NND ideals via their integral closures known in the analytical setting extends to regular local rings. We use the limiting body $\mathcal{C}(\mathcal{I})$ associated to a graded family $\mathcal{I}$ of ideals to provide a new understanding of the celebrated "Multiplicity $=$ Volume" f…

Flirrende Tage.

Seit jeher liegen die ergiebigsten Senffelder der Mark rund um das Kombinat Kettwurst #Prietsch.

[2025-05-30 Fri (UTC), no new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

Ah, a new meaning for Taco Tuesday and Taco Ding Dong...
"Trump’s not happy about Wall Street’s name for tariff flip-flops "
https://www.politico.com/news/2025/05/28/trump-wall-street-acronym-tariffs-00372814

Ah, FFOTUS' judicial appointments reach the bottom of the barrel - even Bork was far better as a judge and more ethical.
"Ex-Trump defense lawyer Emil Bove, a top Justice Department official, is picked to be federal judge"
https://ap…

Ex-Trump lawyer Emil Bove, a top Justice Department official, is picked to be federal judge
President Donald Trump says he's nominating his former criminal defense lawyer Emil Bove to become a federal appeals court judge. As a high-ranking Justice Department official, Bove was behind the controversial move to drop the corruption case against New York City Mayor Eric Adams as well as some of the agency’s most scrutinized actions since Trump’s return to the White House in January. Trump has picked Bove to fill a vacancy on the 3rd U.S. Circuit Court of Appeals, which hears cases fro…

Good - a court slaps down FFOTUS tariffs...
"Court says Trump doesn't have the authority to set tariffs"
https://www.axios.com/2025/05/28/trump-tariffs-trade-court-ruling

Court says Trump doesn't have the authority to set tariffs
The U.S. Court of International Trade's ruling could bring the trade war to a screeching halt.

Has anyone yet tied FFOTUS' "golden dome" to the scene in Game of Thrones where the prince is given a golden crown?
Gold is not a particularly good material from which to make a protective shield or dome.
https://www.youtube.com/watch?v=Fbhv3JHkJNk

Monsieur Hulot parkt neuerdings in der Nachbarschaft.

This https://arxiv.org/abs/2502.10152 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Characterization of Logarithmic Fekete Critical Configurations of at Most Six Points in All Dimensions
We consider the logarithmic Fekete problem, which consists of placing a fixed number of points on the unit sphere in $\mathbb{R}^d$, in such a way that the product of all pairs of mutual Euclidean distances is maximized or, equivalently, so that their logarithmic energy is minimized. Using tools from Computational Algebraic Geometry, we find and classify all critical configurations for this problem when considering at most six points in every dimension $d$. In particular, our approach gives new…

On General Principal Symmetric Ideals
Noah Walker
https://arxiv.org/abs/2505.21802 https://arxiv.org/pdf/2505.21802

On General Principal Symmetric Ideals
In a recent paper by Harada, Seceleanu, and Şega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is sufficiently large. In this paper, we strengthen that result by giving a effective bound on the number of variables needed for their conclusion to hold. The bound is related to a well-known integer sequence involving partition numbers (OEIS A000070). Along the way, we …

[2025-05-29 Thu (UTC), 1 new article found for math.AC Commutative Algebra]
#toXiv_bot_toot

This https://arxiv.org/abs/2502.10152 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Characterization of Logarithmic Fekete Critical Configurations of at Most Six Points in All Dimensions
We consider the logarithmic Fekete problem, which consists of placing a fixed number of points on the unit sphere in $\mathbb{R}^d$, in such a way that the product of all pairs of mutual Euclidean distances is maximized or, equivalently, so that their logarithmic energy is minimized. Using tools from Computational Algebraic Geometry, we find and classify all critical configurations for this problem when considering at most six points in every dimension $d$. In particular, our approach gives new…

Frühes Erröten
oder
Noch zögern die Schnecken.

On General Principal Symmetric Ideals
Noah Walker
https://arxiv.org/abs/2505.21802 https://arxiv.org/pdf/2505.21802

On General Principal Symmetric Ideals
In a recent paper by Harada, Seceleanu, and Şega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is sufficiently large. In this paper, we strengthen that result by giving a effective bound on the number of variables needed for their conclusion to hold. The bound is related to a well-known integer sequence involving partition numbers (OEIS A000070). Along the way, we …

[2025-05-29 Thu (UTC), 1 new article found for math.AC Commutative Algebra]
#toXiv_bot_toot

#HeuteImGarten
24.(!) Mai: Frostschäden an Kartoffeln und Bohnen. ☹️

Ginstergunst im Musenhag.

No code Week Milano
#nocodeweek #NoCode #milano #ncw2025

Hermann-Immobilien, gehobene Ausstattung in traumhaftem Ambiente.

This https://arxiv.org/abs/2307.11489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some properties of the asymptotic Samuel function
The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

[2025-05-28 Wed (UTC), no new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

Der Himmel hält sich raus. #MeerMittwoch

This https://arxiv.org/abs/2311.07308 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graded Betti numbers of a hyperedge ideal associated to join of graphs
Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $r$ be a positive integer. We consider the hypergraph $\mathrm{Con}_r(G)$ whose vertices are the vertices of $G$ and the (hyper)edges are all $A\subseteq V(G)$ such that $|A|=r+1$ and the induced subgraph $G[A]$ is connected. The (hyper)edge ideal $I_r(G)$ of $\mathrm{Con}_r(G)$ is also the Stanley-Reisner ideal of a generalisation of the independence complex of $G$, called the $r$-independence complex $\mathrm{Ind}_r(G…

This https://arxiv.org/abs/2307.11489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some properties of the asymptotic Samuel function
The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

[2025-05-28 Wed (UTC), no new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

#TrainTrackTuesday? Fünf vor zwölf war mal.

This https://arxiv.org/abs/2311.07308 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graded Betti numbers of a hyperedge ideal associated to join of graphs
Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $r$ be a positive integer. We consider the hypergraph $\mathrm{Con}_r(G)$ whose vertices are the vertices of $G$ and the (hyper)edges are all $A\subseteq V(G)$ such that $|A|=r+1$ and the induced subgraph $G[A]$ is connected. The (hyper)edge ideal $I_r(G)$ of $\mathrm{Con}_r(G)$ is also the Stanley-Reisner ideal of a generalisation of the independence complex of $G$, called the $r$-independence complex $\mathrm{Ind}_r(G…

t bestimmt auch öfter die Hutschnur dieser Tage.

Manchmal braucht es keine #Profi-Ausrüstung, sondern nur einen glücklichen Moment 🥰
#Darmstadt
#Mond
#Astrofotografie
#Astrophotography
#Moon
#FujifilmXT30II
#Amateurphotohraphy

Gänseklein.

Squared Linear Models
Hannah Friedman, Bernd Sturmfels, Maximilian Wiesmann
https://arxiv.org/abs/2505.19351 https://arxiv.org/pdf/25…

Squared Linear Models
We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one for each region of the projective hyperplane arrangement. We study the ideal and singular locus of the model, and we give a determinantal presentation for its likelihood correspondence. We characterize tropical degenerations of the MLE, and we describe log-normal polytopes.

S-r-$ideals in Commutative Rings
Abuzer G\"und\"uz, Osama A. Naji, Mehmet \"Ozen
https://arxiv.org/abs/2505.19198 https://

S-r-$ideals in Commutative Rings
This article introduces the notion of $S-r-$ideals in commutative ring $H$ as a generalization of $ r-$ideals. Let $S$ be a multiplicatively closed subset and $A$ an ideal of $H$ with $S\cap A= \emptyset$. $A$ is called $S-r-ideal$ if $ \exists s\in S$ such that for $w,z\in H,\; wz\in A$ and $Ann(w)=0$, then $sz\in A.$ Basic properties of $S-r-$ideals are given. It is shown that an $r-$ideal is always an $S-r-$ideal, and the converse is true under some conditions. Various characterizations of $…

Betti numbers and almost complete intersection monomial ideals
Amir Mafi, Rando Rasul Qadir
https://arxiv.org/abs/2505.18788 https://…

Betti numbers and almost complete intersection monomial ideals
Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $I$ be a monomial ideal of $R$. In this paper, we present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals.

An Early History of Toric Ideals
Serkan Ho\c{s}ten
https://arxiv.org/abs/2505.18443 https://arxiv.org/pdf/2505.18443

An Early History of Toric Ideals
Toric ideals are everywhere. They have been in the commutative algebra lexicon since about 1990 when Bernd Sturmfels used the term. The early days of toric ideals and their Gröbner bases were full of new results and promising developments in their applications. Bernd has been consistently their biggest promoter through his own work and that of his collaborators and students. This article is a personal and subjective recalling of the first decade of toric ideals when Bernd played a central role.

[2025-05-27 Tue (UTC), 4 new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

Squared Linear Models
Hannah Friedman, Bernd Sturmfels, Maximilian Wiesmann
https://arxiv.org/abs/2505.19351 https://arxiv.org/pdf/25…

Squared Linear Models
We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one for each region of the projective hyperplane arrangement. We study the ideal and singular locus of the model, and we give a determinantal presentation for its likelihood correspondence. We characterize tropical degenerations of the MLE, and we describe log-normal polytopes.

S-r-$ideals in Commutative Rings
Abuzer G\"und\"uz, Osama A. Naji, Mehmet \"Ozen
https://arxiv.org/abs/2505.19198 https://

S-r-$ideals in Commutative Rings
This article introduces the notion of $S-r-$ideals in commutative ring $H$ as a generalization of $ r-$ideals. Let $S$ be a multiplicatively closed subset and $A$ an ideal of $H$ with $S\cap A= \emptyset$. $A$ is called $S-r-ideal$ if $ \exists s\in S$ such that for $w,z\in H,\; wz\in A$ and $Ann(w)=0$, then $sz\in A.$ Basic properties of $S-r-$ideals are given. It is shown that an $r-$ideal is always an $S-r-$ideal, and the converse is true under some conditions. Various characterizations of $…

Betti numbers and almost complete intersection monomial ideals
Amir Mafi, Rando Rasul Qadir
https://arxiv.org/abs/2505.18788 https://…

Betti numbers and almost complete intersection monomial ideals
Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $I$ be a monomial ideal of $R$. In this paper, we present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals.

An Early History of Toric Ideals
Serkan Ho\c{s}ten
https://arxiv.org/abs/2505.18443 https://arxiv.org/pdf/2505.18443

An Early History of Toric Ideals
Toric ideals are everywhere. They have been in the commutative algebra lexicon since about 1990 when Bernd Sturmfels used the term. The early days of toric ideals and their Gröbner bases were full of new results and promising developments in their applications. Bernd has been consistently their biggest promoter through his own work and that of his collaborators and students. This article is a personal and subjective recalling of the first decade of toric ideals when Bernd played a central role.

[2025-05-27 Tue (UTC), 4 new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

This https://arxiv.org/abs/2412.15368 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sifted degrees of the equations of the Rees module and their connection with the Artin-Rees numbers
Let $A$ be a noetherian ring, $I$ an ideal of $A$ and $N\subset M$ finitely generated $A$-modules. The relation type of $I$ with respect to $M$, denoted by ${\bf rt}\,(I;M)$, is the maximal degree in a minimal generating set of relations of the Rees module ${\bf R}(I;M)=\oplus_{n\geq 0}I^nM$. It is a well-known invariant that gives a first measure of the complexity of ${\bf R}(I;M)$. To help to measure this complexity, we introduce the sifted type of ${\bf R}(I;M)$, denoted by ${\bf st}\,(I;M)$…

This https://arxiv.org/abs/2310.14134 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Endomorphism algebras over commutative rings and torsion in self tensor products
Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products in the case where $\operatorname{End}_R(M)$ has an $R^*$-algebra structure, and prove that if $M$ is indecomposable, then $M \otimes_{\operatorname{End}_R(M)} M$ must always have torsion in this case under mild hypotheses.

On a Relation between Euler characteristics of \MakeLowercase{de} Rham cohomology and Koszul cohomology of graded local cohomology modules
Tony J. Puthenpurakal, Rakesh B. T. Reddy
https://arxiv.org/abs/2505.17597

On a Relation between Euler characteristics of \MakeLowercase{de} Rham cohomology and Koszul cohomology of graded local cohomology modules
Let $K$ be a field of characteristic zero. Let $R = K[X_0, X_1,\ldots,X_n]$ be standard graded. Let $A_{n+1}(K)$ be the $(n + 1)^{th}$ Weyl algebra over $K$. Let $I$ be a homogeneous ideal of $R$ and let $M = H^i_I(R)$ for some $i \geq 0$. By a result of Lyubeznik, $M$ is a graded holonomic $A_{n +1}(K)$-module for each $i \geq 0$. Let $χ^c(\mathbf{\partial}, M)$ ($χ^c(\mathbf{X}, M)$) be the Euler characteristics of de Rham cohomology (resp. Koszul cohomology) of $M$. We prove $χ^c(\mathb…

Ordinary and symbolic powers of matroids via polarization
Justin Lyle, Paolo Mantero
https://arxiv.org/abs/2505.17398 https://arxiv.o…

Ordinary and symbolic powers of matroids via polarization
In this paper, we propose a uniform approach to tackle problems about squarefree monomial ideals whose powers have good properties. We employ this approach to achieve a twofold goal: (i) recover and extend several well--known results in the literature, especially regarding Stanley--Reisner ideals of matroids, and (ii) provide short, elementary proofs for these results. Among them, we provide simple proofs of two celebrated results of Minh and Trung, Varbaro, and Terai and Trung elegantly charac…

[2025-05-26 Mon (UTC), 2 new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

This https://arxiv.org/abs/2412.15368 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sifted degrees of the equations of the Rees module and their connection with the Artin-Rees numbers
Let $A$ be a noetherian ring, $I$ an ideal of $A$ and $N\subset M$ finitely generated $A$-modules. The relation type of $I$ with respect to $M$, denoted by ${\bf rt}\,(I;M)$, is the maximal degree in a minimal generating set of relations of the Rees module ${\bf R}(I;M)=\oplus_{n\geq 0}I^nM$. It is a well-known invariant that gives a first measure of the complexity of ${\bf R}(I;M)$. To help to measure this complexity, we introduce the sifted type of ${\bf R}(I;M)$, denoted by ${\bf st}\,(I;M)$…

This https://arxiv.org/abs/2310.14134 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Endomorphism algebras over commutative rings and torsion in self tensor products
Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products in the case where $\operatorname{End}_R(M)$ has an $R^*$-algebra structure, and prove that if $M$ is indecomposable, then $M \otimes_{\operatorname{End}_R(M)} M$ must always have torsion in this case under mild hypotheses.

On a Relation between Euler characteristics of \MakeLowercase{de} Rham cohomology and Koszul cohomology of graded local cohomology modules
Tony J. Puthenpurakal, Rakesh B. T. Reddy
https://arxiv.org/abs/2505.17597

On a Relation between Euler characteristics of \MakeLowercase{de} Rham cohomology and Koszul cohomology of graded local cohomology modules
Let $K$ be a field of characteristic zero. Let $R = K[X_0, X_1,\ldots,X_n]$ be standard graded. Let $A_{n+1}(K)$ be the $(n + 1)^{th}$ Weyl algebra over $K$. Let $I$ be a homogeneous ideal of $R$ and let $M = H^i_I(R)$ for some $i \geq 0$. By a result of Lyubeznik, $M$ is a graded holonomic $A_{n +1}(K)$-module for each $i \geq 0$. Let $χ^c(\mathbf{\partial}, M)$ ($χ^c(\mathbf{X}, M)$) be the Euler characteristics of de Rham cohomology (resp. Koszul cohomology) of $M$. We prove $χ^c(\mathb…

Ordinary and symbolic powers of matroids via polarization
Justin Lyle, Paolo Mantero
https://arxiv.org/abs/2505.17398 https://arxiv.o…

Ordinary and symbolic powers of matroids via polarization
In this paper, we propose a uniform approach to tackle problems about squarefree monomial ideals whose powers have good properties. We employ this approach to achieve a twofold goal: (i) recover and extend several well--known results in the literature, especially regarding Stanley--Reisner ideals of matroids, and (ii) provide short, elementary proofs for these results. Among them, we provide simple proofs of two celebrated results of Minh and Trung, Varbaro, and Terai and Trung elegantly charac…

[2025-05-26 Mon (UTC), 2 new articles found for math.AC Commutative Algebra]
#toXiv_bot_toot

This https://arxiv.org/abs/2505.15707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

When are syzygies of the residue field self-dual?
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao characterized Arf local rings as exactly those one-dimensional Cohen--Macaulay local rings over which every finitely generated reflexive module is self-dual, and raised the general question of characterizing rings over which every finitely generated reflexive module…

This https://arxiv.org/abs/2504.02966 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On deformation of perfectoid purity in Gorenstein domains
If $(R,\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation…

This https://arxiv.org/abs/2407.19999 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Auslander-Reiten annihilators
The Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely generated module is projective when certain Ext-modules vanish. But what if those Ext-modules do not vanish? We study the annihilators of these Ext-modules and formulate a generalisation of the Auslander-Reiten Conjecture. We prove this general version for high syzygies of modules over several classes of rings including analytically unramified Arf rings, 2-dimensional local normal domains with rational sin…

This https://arxiv.org/abs/2505.15707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

When are syzygies of the residue field self-dual?
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao characterized Arf local rings as exactly those one-dimensional Cohen--Macaulay local rings over which every finitely generated reflexive module is self-dual, and raised the general question of characterizing rings over which every finitely generated reflexive module…

This https://arxiv.org/abs/2504.02966 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On deformation of perfectoid purity in Gorenstein domains
If $(R,\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation…

This https://arxiv.org/abs/2407.19999 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Auslander-Reiten annihilators
The Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely generated module is projective when certain Ext-modules vanish. But what if those Ext-modules do not vanish? We study the annihilators of these Ext-modules and formulate a generalisation of the Auslander-Reiten Conjecture. We prove this general version for high syzygies of modules over several classes of rings including analytically unramified Arf rings, 2-dimensional local normal domains with rational sin…