McKay correspondence for symplectic quotient singularities

Details McKay correspondence for symplectic quotient singularities McKay correspondence for symplectic quotient singularities

1999-07-13

arxiv.org/abs/math/9907087v2

Mathematics

Algebraic Geometry

28 pages, LaTeX2e; added new references and corrected a proof (of Proposition 4.1)

Scientific paper

We consider the quotients $X = V/G$ of a symplectic complex vector space $V$ by a finite subgroup $G \subset Sp(V)$ which admit a smooth crepant resolution $Y \to X$. For such quotients, we prove the homological McKay correspondence conjectured by M. Reid. Namely, we construct a natural basis in the homology space $H_\cdot(Y,\Q)$ whose elements are numbered by the conjugacy classes in the finite group $G$.

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