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arXiv · 1912.01689

Comparing the Kirwan and noncommutative resolutions of quotient varieties

Špela Špenko·Michel Van den Bergh
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Abstract

Let a reductive group $G$ act on a smooth variety $X$ such that a good quotient $X{/\!\!/}G$ exists. We show that the derived category of a noncommutative crepant resolution (NCCR) of $X{/\!\!/} G$, obtained from a $G$-equivariant vector bundle on $X$, can be embedded in the derived category of the (canonical, stacky) Kirwan resolution of $X{/\!\!/} G$. 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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Špela Špenko, Michel Van den Bergh. 2019-12-03. Comparing the Kirwan and noncommutative resolutions of quotient varieties. https://arxiv.org/abs/1912.01689

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