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Comparing the Kirwan and noncommutative resolutions of quotient varieties (1912.01689v1)
Published 3 Dec 2019 in math.AG, math.RA, and math.RT
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.