Dynkin diagrams and crepant resolutions of quotient singularities

Details Dynkin diagrams and crepant resolutions of quotient singularities Dynkin diagrams and crepant resolutions of quotient singularities

1999-03-27

arxiv.org/abs/math/9903157v1

Mathematics

Algebraic Geometry

30 pages, LaTeX2e

Scientific paper

Let $V$ be a complex vector space on which a finite group $G$ acts by linear transformations. Let $W = V \oplus V^*$ be the sum of $V$ with its dual $V^*$. We prove that if the quotient $W/G$ admits a smooth crepant resolution, then the subgroup $G \subset Aut V$ is generated by complex reflections. We also obtain some results on the structure of smooth crepant resolutions of the quotients $W/G$, where $W$ is a symplectic vector space, and $G \subset Aut W$ is a finite group of symplectic linear transformations of the vector space $W$.

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