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@article{Negron:2020:10.1016/j.aim.2020.106978,
author = {Negron, C and Schedler, T},
doi = {10.1016/j.aim.2020.106978},
journal = {Advances in Mathematics},
pages = {1--49},
title = {The Hochschild cohomology ring of a global quotient orbifold},
url = {http://dx.doi.org/10.1016/j.aim.2020.106978},
volume = {364},
year = {2020}
}

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TY  - JOUR
AB  - We study the cup product on the Hochschild cohomology of the stack quotient  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 , under a natural filtration. This sheaf is an algebra over the polyvector fields  on X, and is generated as a -algebra by the sum of the determinants  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 , which requires (for the cup product) a nontrivial normalization missing in previous literature
AU  - Negron,C
AU  - Schedler,T
DO  - 10.1016/j.aim.2020.106978
EP  - 49
PY  - 2020///
SN  - 0001-8708
SP  - 1
TI  - The Hochschild cohomology ring of a global quotient orbifold
T2  - Advances in Mathematics
UR  - http://dx.doi.org/10.1016/j.aim.2020.106978
UR  - https://www.sciencedirect.com/science/article/pii/S0001870820300037?via%3Dihub
UR  - http://hdl.handle.net/10044/1/76872
VL  - 364
ER  -

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