The Hochschild cohomology ring of a global quotient orbifold
The Hochschild cohomology ring of a global quotient orbifold
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全局商轨道折叠的 Hochschild 上同调环
DOI：
10.1016/j.aim.2020.106978
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发表时间：
2018
影响因子：
1.7
通讯作者：
P. Etingof
中科院分区：
文献类型：
--
作者：
C. Negron;T. Schedler;Pieter Belmans;P. Etingof
研究了光滑拟投射簇X的叠商[X/G]与有限群G的Hochschild上同调的杯积.更具体地说，我们构造了一个G-等变层的分次代数X的G-不变的整体部分恢复相关的分次代数的Hochschild上同调[X/G]，在一个自然的过滤。这个层是X上的多向量场T X p o l y上的一个代数，并且由X中固定轨迹的法丛的行列式det（N X g）的和生成为T X p o l y-代数。我们用我们的理解Hochschild上同调的结论是，类似的Kontsevich的形式定理，杯产品，不持有德利涅-芒福德栈一般。讨论了辛簇X上的辛群作用与轨道上同调和阮氏上同调的关系。在描述的Hochschild上同调的辛的情况下，我们采用兼容trivializations的决定因素det（N X g），这需要（杯产品）一个非平凡的归一化在以前的文献中丢失。
We study the cup product on the Hochschild cohomology of the stack quotient [X/G] of a smooth quasi-projective variety X by a finite group G. More specifically, we construct a G-equivariant sheaf of graded algebras on X whose G-invariant global sections recover the associated graded algebra of the Hochschild cohomology of [X/G], under a natural filtration. This sheaf is an algebra over the polyvector fields T X p o l y on X, and is generated as a T X p o l y-algebra by the sum of the determinants det(N X g) of the normal bundles of the fixed loci in X. We employ our understanding of Hochschild cohomology to conclude that the analog of Kontsevich's formality theorem, for the cup product, does not hold for Deligne–Mumford stacks in general. We discuss, in the case of a symplectic group action on a symplectic variety X, relationships with orbifold cohomology and Ruan's cohomological conjectures. In describing the Hochschild cohomology in the symplectic situation, we employ compatible trivializations of the determinants det(N X g), which requires (for the cup product) a nontrivial normalization missing in previous literature.
派生交集的形式和轨道 HKR 同构
影响因子：
0.9
作者：
Arinkin, Dima;Căldăraru, Andrei;Hablicsek, Márton
通讯作者：
Hablicsek, Márton