Comparing the Kirwan and noncommutative resolutions of quotient varieties
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 semiorthogonal decomposition in which the other parts are all derived categories of Azumaya algebras over smooth DeligneMumford stacks.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.01689
 Bibcode:
 2019arXiv191201689S
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Rings and Algebras;
 Mathematics  Representation Theory
 EPrint:
 40 pages