通过 LLV 代数衍生出的超凯勒流形类别。

IF 1.2 3区数学 Q1 MATHEMATICS

Milan Journal of Mathematics Pub Date : 2022-01-01 Epub Date: 2022-06-21 DOI:10.1007/s00032-022-00358-x

T Beckmann

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引用次数: 0

摘要

我们主要回顾了泰尔曼（Derived equivalences of hyperkähler varieties, 2019, arXiv:1906.08081）关于超凯勒流形派生范畴的工作。我们利用多向量场研究 LLV 代数，证明它是一个派生不变量。我们还给出了派生等价物对同调的作用及其霍奇结构研究的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra.

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Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra.

We mostly review work of Taelman (Derived equivalences of hyperkähler varieties, 2019, arXiv:1906.08081) on derived categories of hyper-Kähler manifolds. We study the LLV algebra using polyvector fields to prove that it is a derived invariant. Applications to the action of derived equivalences on cohomology and to the study of their Hodge structures are given.

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来源期刊

Milan Journal of Mathematics 数学-数学

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists. Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.