Tootfinder

Dubrovin-Natanzon divisors on MM-curves
Simonetta Abenda, Petr G. Grinevich
https://arxiv.org/abs/2508.08426 https://arxiv.org/pdf/2508.08426

Dubrovin-Natanzon divisors on MM-curves
${\mathtt{MM}}$-curves are rational degenerations of ${\mathtt{M}}$-curves, i.e. they are maximal Mumford in the sense that they posses $g$ tropical cycles and exactly $g+1$ real ovals, where $g$ is the arithmetic genus. For rational curves the ``naive'' definition of divisors as formal sums of points requires a refinement. In the finite-gap theory of KP II equation the real regular solutions correspond to the Dubrovin-Natanzon (DN) divisors on ${\mathtt{M}}$-curves. In the case of real regular…

Så er mit interview under Verden ForsŸgt Forklaret kommet ud:
“Trusselsbreve og terrormanifester: Hvad ordvalget afslŸrer”
https://youtu.be/WqODChT7TSg?si=ddvXr2Uk8CiKsLe2
(Jeg opdagede det kun fordi en - mig ubekendt - mand har skrevet en hademail til mig om det. Han vi…

The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors
Masataka Iwai, Satoshi Jinnouchi, Shiyu Zhang
https://arxiv.org/abs/2507.08522

The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors
We establish the Miyaoka-Yau inequality for $n$-dimensional projective klt varieties with big canonical divisor $K_X$: \[ (2(n+1)\widehat{c}_2(X) - n \widehat{c}_1(X)^2) \cdot \langle c_1(K_X)^{n-2} \rangle \ge 0. \] We also prove the Miyaoka-Yau inequality for K-semistable projective klt varieties with big anticanonical divisor $-K_X$. As part of our approach, we define the non-pluripolar product $\langle α_1 \cdots α_p \rangle$ on singular varieties, and establish the Bogomolov-Gieseker typ…

heise | Diffusers: Wie Sie Bilder mit Python und KI lokal generieren und verändern
Mit der freien Bibliothek Diffusers von Hugging Face kann Python lokal neue Bilder erzeugen, vorhandene in einem anderen Stil ausgeben oder sie bearbeiten.

A New Classification of Positive Integers Via New Divisor Functions
Brahim Mittou
https://arxiv.org/abs/2509.08844 https://arxiv.org/pdf/2509.08844

A New Classification of Positive Integers Via New Divisor Functions
Let $d_1 = 1 < d_2 < d_3 < \cdots < d_{τ(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. In this paper, for real or complex values of $α$, we define and study some properties of two new divisor functions $σ_{e,α}$ and $σ_{o,α}$. The first computes the sum of the $α$-th powers of the divisors of $n$ with even indices, and the second computes the sum of the $α$-th powers of the divisors of $n$ with odd indices. We also introduce a new type of positive in…

The orange pedophile wants us to stop talking about his groomer.
He seems a bit pissed.
https://fed.brid.gy/r/https://bsky.app/profile/did:plc:65neilruzq2tnxdqcupghsov/post/3lttvatz3lk2b

Dorean Paxorales (@dpaxorales.bsky.social)
#streisandeffect

On the strong metric dimension of the complement of the zero-divisor graph of a lattice
Pravin Gadge, Vinayak Joshi
https://arxiv.org/abs/2508.05809 https://

On the strong metric dimension of the complement of the zero-divisor graph of a lattice
In this paper, we compute the strong metric dimension of the complement of the zero-divisor graph of the blow-up of a Boolean lattice. Using these results, we calculate the strong metric dimension of the total graph, the maximal graph, the intersection graph of ideals, the complement of the zero-divisor graph of a reduced ring, and the component graph of a vector space.

Superior Highly Composite Numbers and the Explicit Upper Bound of Generalized Divisor Functions
Lee-Peng Teo
https://arxiv.org/abs/2508.06764 https://arxiv…

Superior Highly Composite Numbers and the Explicit Upper Bound of Generalized Divisor Functions
For $k\geq 2$, we give a detailed exposition of the superior $k$-highly composite numbers. We then consider the function \[f_k(n)=\frac{\log d_k(n)\log\log n}{\log k\log n},\quad n\geq 3\] which has a maximum value $λ(k)$ at a superior $k$-highly composite number. We develop an efficient algorithm to compute $λ(k)$ and the positive integer $N_{\max}(k)$ where $f_k$ achieves the value $λ(k)$. The results for $2\leq k\leq 100$ are tabled.

Smoothed Shifted Convolutions of Generalised Divisor Functions
Cheuk Fung Lau
https://arxiv.org/abs/2509.07556 https://arxiv.org/pdf/2509.07556

Smoothed Shifted Convolutions of Generalised Divisor Functions
We prove an asymptotic formula for the smoothed shifted convolution of the generalised divisor function $d_k(n)$ and the divisor function $d(n)$, with a power-saving error term independent of $k$. In particular, when $k$ is large, this is an improvement on Topacogullari (2018).

Totally real divisors on curves
Lorenzo Baldi, Mario Kummer, Daniel Plaumann
https://arxiv.org/abs/2509.07544 https://arxiv.org/pdf/2509.07544

Totally real divisors on curves
Since the works of Krasnov and Scheiderer, there has been an interest in studying effective totally real divisors on a curve X defined over a real closed field, i.e., effective divisors supported on the real locus. Scheiderer proved that, for smooth curves over the real numbers with nonempty real locus, each divisor of sufficiently high degree is linearly equivalent to an effective totally real one. The smallest degree N(X) with this property is called the totally real divisor threshold. When…