McKay equivalence for symplectic resolutions of singularities

Details McKay equivalence for symplectic resolutions of singularities McKay equivalence for symplectic resolutions of singularities

2004-01-01

arxiv.org/abs/math/0401002v1

Mathematics

Algebraic Geometry

LaTeX2e, 29 pages. Dedicated to the memory of A.N. Tyurin. Russian version available at http://imperium.lenin.ru/~kaledin/tex/

Scientific paper

Let $V$ be a finite-dimensional symplectic vector space over a field of
characteristic 0, and let $G \subset Sp(V)$ be a finite subgroup. We prove that
for any crepant resolution $X \to V/G$, the bounded derived category
$D^b(Coh(X))$ of coherent sheaves on $X$ is equivalent to the bounded derived
category $D^b_G(Coh(V))$ of $G$-equivariant coherent sheaves on $V$.

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