Atomic objects on hyper-Kähler manifolds

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2024-04-19 DOI:10.1090/jag/830

Thorsten Beckmann

引用次数: 2

Abstract

We introduce and study the notion of atomic sheaves and complexes on higher-dimensional hyper-Kähler manifolds and show that they share many of the intriguing properties of simple sheaves on K3 surfaces. For example, we prove formality of the dg algebra of derived endomorphisms for stable atomic bundles. We further demonstrate the characteristics of atomic objects by studying atomic Lagrangian submanifolds. In the appendix, we prove nonexistence results for spherical objects on hyper-Kähler manifolds.

查看原文本刊更多论文

超凯勒流形上的原子物体

我们介绍并研究了高维超凯勒流形上的原子卷和复数概念，并证明它们与 K3 曲面上的简单卷具有许多共同的有趣性质。例如，我们证明了稳定原子束的派生内态量 dg 代数的形式性。我们通过研究原子拉格朗日子线面进一步证明了原子对象的特性。在附录中，我们证明了超凯勒流形上球面对象的非存在性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.