Comparing the Kirwan and noncommutative resolutions of quotient varieties

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-22 DOI:10.1515/crelle-2023-0024

S. Spenko, Michel van den Bergh

引用次数: 0

Abstract

Abstract Let a reductive group G act on a smooth variety X such that a good quotient X / / G {X/\!\!/G} exists. We show that the derived category of a noncommutative crepant resolution (NCCR) of X / / G {X/\!\!/G} , obtained from a G-equivariant vector bundle on X, can be embedded in the derived category of the (canonical, stacky) Kirwan resolution of X / / G {X/\!\!/G} . In fact, the embedding can be completed to a semi-orthogonal decomposition in which the other parts are all derived categories of Azumaya algebras over smooth Deligne–Mumford stacks.

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比较商变量的柯湾分辨和非交换分辨

摘要:令约化群G作用于光滑变量X，使得良商X/ / G {X/\!\!/ G}的存在。我们证明了X/ / G {X/\!\!/G}，由X上的G等变向量束得到，可以嵌入到X/ /G {X/\!\!/ G}。事实上，嵌入可以完成为半正交分解，其中其他部分都是光滑Deligne-Mumford叠上的Azumaya代数的派生范畴。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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