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Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures

本文研究了 admitting 零维纤维周期映射的复极化变体 Hodge 结构的拟紧 Kähler 流形 $U$ ，证明了其具有代数双曲性并满足广义大 Picard 定理，且存在有限 étale 覆盖使得其任意射影紧化在边界外具有 Picard 双曲性且非边界子簇均为一般型，从而推广了 Nadel、Rousseau、Brunebarbe 和 Cadorel 关于有界对称域商空间紧化双曲性的相关工作。

Ya Deng2026-03-11🔢 math

On the dual positive cones and the algebraicity of a compact Kähler manifold

本文证明了若紧凯勒流形的对偶凯勒锥包含一个有理内点，则其阿尔巴内塞簇是射影的，从而解决了里奇平坦紧凯勒流形的 Oguiso-Peternell 问题，并研究了三维流形的相关代数性问题。

Hsueh-Yung Lin2026-03-11🔢 math

Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class

本文通过构造群论版的 Johnson/Morita 上同调类并将其应用于光滑曲线的 pro-l 平展基本群，揭示了其与 Hain 和 Matsumoto 工作的联系，并据此构造了一个非超椭圆曲线，其 Ceresa 类在 l 进 Abel-Jacobi 映射下的像具有挠性。

Dean Bisogno, Wanlin Li, Daniel Litt + 1 more2026-03-11🔢 math

Ulam numbers have zero density

本文证明了 Ulam 数的自然密度为零，即当上限趋于无穷大时，Ulam 数在自然数中的占比趋于零。

Theophilus Agama2026-03-11🔢 math

Uniform K-stability of polarized spherical varieties

本文通过将极化球面簇的 K-稳定性表述为组合数据，建立了 G-一致 K-稳定性的组合充分条件，从而为常数量曲率凯勒度量的存在性提供了可显式检验的判据，并揭示了在特定条件下 G-一致 K-稳定性与 G-等变测试构型下的 K-多项式稳定性的等价性。

Thibaut Delcroix2026-03-11🔢 math

Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic

本文证明了在正特征代数闭域上，若光滑射影簇 $X$ 到 $T$ 的满射具有几何整且非有理连通的通纤维，则相对典则除子 $K_{X/T}$ 是伪有效的，其证明核心在于构造基底的有限非有理连通覆盖，并确立了基于上同调维数条件的非有理连通性判别准则。

Zsolt Patakfalvi2026-03-11🔢 math

Stably semiorthogonally indecomposable varieties

本文引入了非交换稳定半正交不可分解（NSSI）簇的概念，证明了具有有限阿尔巴内塞映射的簇及满足特定纤维化条件的簇均具有该性质，并由此推导出包括 $C \times \mathbb{P}^1$ 在内的某些簇不存在幽灵子范畴。

Dmitrii Pirozhkov2026-03-11🔢 math

On singular Hilbert schemes of points: Local structures and tautological sheaves

本文通过建立 Thomason 不动点定理的内蕴版本并确定 $\mathbb{A}^3$ 中至多 7 个点希尔伯特概型的局部结构，计算了奇点处的等变希尔伯特函数，进而验证了关于 $\mathbb{P}^3$ 上至多 6 个点希尔伯特概型上典则层欧拉示性数的 Zhou 猜想。

Xiaowen Hu2026-03-11🔢 math

Filtered formal groups, Cartier duality, and derived algebraic geometry

本文在滤过设定下构建了形式群概念并描述其与特定滤过 Hopf 代数之间的对偶关系，利用导出代数几何中的法锥变形技术证明了相关滤过的唯一性，进而恢复了滤过圆上的滤过结构并将 $\widehat{\mathbb{G}}$ -Hochschild 同调不变量提升至谱代数几何框架。

Tasos Moulinos2026-03-11🔢 math

Functionality for isomorphism classes of curves and hypersurfaces

本文描述了基于不变量理论的算法，用于解决主要涉及 genus 2、3 和 4 的曲线及超曲面的几何同构类问题，并包含了基于第一作者博士论文的新理论成果。

Thomas Bouchet, Reynald Lercier, Jeroen Sijsling, Christophe Ritzenthaler2026-03-11🔢 math

Cohomology classes of complex approximable algebras

本文证明了在复数域上，Huayi Chen 提出的可逼近分次代数所关联的无穷维 Weil 除子必然具有有限的上同调类。

Catriona Maclean2026-03-11🔢 math

Trace formalism for motivic cohomology

本文旨在为 Voevodsky、Ayoub 及 Cisinski-Déglise 建立的动机上同调六函子形式构造迹映射及其 $\infty$ -提升，并通过利用 Suslin-Voevodsky 的相对循环群以更函子化的方式重新诠释该迹形式。

Tomoyuki Abe2026-03-11🔢 math

On a decomposition of $p$ -adic Coxeter orbits

本文研究了非阿基米德局部场上无挠约化群 ${\bf G}$ 的 $p$ -adic Deligne--Lusztig 空间 $X_w(b)$ 的几何性质，证明了当 ${\bf G}$ 为经典群、 $b$ 为基本且 $w$ 为 Coxeter 元素时，该空间可分解为特定积分 $p$ -adic Deligne--Lusztig 空间的平移并集，并在此过程中将 DeBacker 和 Reeder 关于无挠环面有理共轭类的观察推广至扩展纯内形式情形，同时证明了 Frobenius 扭曲 Steinberg 横截面的回路版本。

Alexander B. Ivanov2026-03-11🔢 math

math

Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures

On the dual positive cones and the algebraicity of a compact Kähler manifold

Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class

Ulam numbers have zero density

Uniform K-stability of polarized spherical varieties

Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic

Stably semiorthogonally indecomposable varieties

On singular Hilbert schemes of points: Local structures and tautological sheaves

Filtered formal groups, Cartier duality, and derived algebraic geometry

Functionality for isomorphism classes of curves and hypersurfaces

Cohomology classes of complex approximable algebras

Trace formalism for motivic cohomology

On a decomposition of $p$ -adic Coxeter orbits

On equations of fake projective planes with automorphism group of order $21$

Algebraic subgroups of the group of birational transformations of ruled surfaces

Logarithmic resolution via multi-weighted blow-ups

Torus Actions on Quotients of Affine Spaces

Affine Subspace Concentration Conditions

Perverse-Hodge complexes for Lagrangian fibrations

On the Existence of Balanced Generalized de Bruijn Sequences

math

Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures

On the dual positive cones and the algebraicity of a compact Kähler manifold

Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class

Ulam numbers have zero density

Uniform K-stability of polarized spherical varieties

Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic

Stably semiorthogonally indecomposable varieties

On singular Hilbert schemes of points: Local structures and tautological sheaves

Filtered formal groups, Cartier duality, and derived algebraic geometry

Functionality for isomorphism classes of curves and hypersurfaces

Cohomology classes of complex approximable algebras

Trace formalism for motivic cohomology

On a decomposition of ppp-adic Coxeter orbits

On equations of fake projective planes with automorphism group of order $21$

Algebraic subgroups of the group of birational transformations of ruled surfaces

Logarithmic resolution via multi-weighted blow-ups

Torus Actions on Quotients of Affine Spaces

Affine Subspace Concentration Conditions

Perverse-Hodge complexes for Lagrangian fibrations

On the Existence of Balanced Generalized de Bruijn Sequences

On a decomposition of $p$ -adic Coxeter orbits