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Generic models of licci ideals parametrized by Schur functors
Lorenzo Guerrieri, Xianglong Ni, Jerzy Weyman
https://arxiv.org/abs/2506.09598 https://

Generic models of licci ideals parametrized by Schur functors
Let R be a commutative Noetherian ring. Licci ideals are the ideals of R that can be linked in a finite number of steps to a complete intersection. Each licci ideal admits a rigid deformation, and two licci ideals are in the same Herzog class if they have a common deformation. In this work, we show how all the Herzog classes of licci ideals of codimension 3 can be parametrized in terms of pairs of partitions associated to Schur functors. This fact allows to describe in a purely combinatorial wa…

Structural results on idealistic equivalence relations
Filippo Calderoni, Luca Motto Ros
https://arxiv.org/abs/2506.08217 https://arx…

Structural results on idealistic equivalence relations
We address some fundamental problems concerning the structure of idealistic equivalence relations. In particular, we show that, under analytic determinacy, there are continuum many idealistic analytic equivalence relations that are not classwise Borel isomorphic to an orbit equivalence relation. Moreover, we also discuss alternative formulations of the E1 conjecture, and present an elementary counterexample to one of its earliest variants proposed by Hjorth and Kechris in 1997.

Errol Musk, the father of U.S. billionaire Elon Musk,
has arrived in Moscow to attend the Forum of the Future 2050,
a pro-Kremlin event scheduled for June 9-10,  the Russian newspaper Kommersant reported on June 8.
https://kyivindepend…

Elon Musk's father to attend pro-Kremlin event in Russia hosted by far-right ideologue
Among the forum's panels are sessions titled "Russian Space: The Race for Mars" and "The Battle for Hearts and Minds: The Ideology of Sovereign Russia."

@… Sin embargo, quienes buscaban atraer la atención del público eran sensibles a los deseos de la gente, así que ignoraron deliberadamente estos ideales y crearon listas pršcticas de servidores, recomendando personalmente algun…

$\operatorname{v}$-numbers of integral closure filtrations of monomial ideals
Vanmathi A, Parangama Sarkar
https://arxiv.org/abs/2506.09051 https://…

$\operatorname{v}$-numbers of integral closure filtrations of monomial ideals
In this article, we investigate the $\operatorname{v}$-numbers of powers of monomial ideals and their integral closures in a polynomial ring $S$. We provide an alternative proof for determining the $\operatorname{v}$-numbers of powers of complete intersection monomial ideals. Furthermore, we analyze the $\operatorname{v}$-numbers associated to integral closure filtrations of irreducible monomial ideals and explore their relationship with the Castelnuovo-Mumford regularity of these ideals. Conse…

On ideals of product of commutative rings and their applications
Mehdi Badie, Ali Rezaie Aliabad, Foad Obeidavi
https://arxiv.org/abs/2506.08537 https://…

On ideals of product of commutative rings and their applications
In this paper, leveraging the recent achievements of researchers, we have revisited the family of ideals of product of commutative rings. We demonstrate that if $ \{ R_α\}_{α\in A} $ is an infinite family of rings, then $ \left| Max \left( \prod_{α\in A} R_α\right) \right| \geqslant 2^{2^{|A|}} $. Notably, if these rings are local then the equality holds. We establish that $ Max(R_α) $ is homeomorphic to a closed subset of $ Max \left( \prod_{α\in A} R_α\right) $, for…

Intressant i "Älskade politik" om hur regeringskansliet numera försöker stoppa "paper trails" i många fall – och de "ideologiska skälen" till stoppet för Unrwa-stödet. https://www.dn.se/podd/alskade-politik/tomtar-och-t…

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Jag reflekterar över varför jag gör det jag gör och hur jag vill nyttja min tid. Mitt skrivande är mitt kall, och tillsammans med mina modeller och visualiseringar är det så just jag kan bidra. Nu kan du som vill och har förmåga också backa det arbetet.

"År 1973 skrev Ursula K. Le Guin sin prisbelönta berättelse De som går bort från Omelas. Denna korta science fiction-berättelse beskriver en idyllisk stad, Omelas, där alla mä…

Ideals generated by corner-interval minors
Marie Amalore Nambi
https://arxiv.org/abs/2506.09618 https://arxiv.org/pdf/2506.09618

Ideals generated by corner-interval minors
In this article, we study binomial ideals generated by an arbitrary collection of corner-interval $2$-minors of a generic matrix. We determine the minimal prime ideals of such ideals and characterize their radicality in the special case of corner minors. Moreover, we discuss connectivity properties of contingency tables in algebraic statistics. We compute the Hilbert-Poincaré polynomial of the ideal generated by the set of all corner-interval minors and we derive the formula for the regularity…

This https://arxiv.org/abs/2312.01613 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Binomial Edge Ideals of Complements of Graphs of Girth at Least 5
We calculate the local cohomology modules of the binomial edge ideals of the complements of graphs of girth at least 5 using the tools introduced by Àlvarez Montaner in arXiv:1901.08645. We then use this calculation to compute the depth, dimension, and regularity of these binomial edge ideals.