Holomorphic symplectic geometry and orbifold singularities

Details Holomorphic symplectic geometry and orbifold singularities Holomorphic symplectic geometry and orbifold singularities

1999-03-30

arxiv.org/abs/math/9903175v3

Asian J. Math. 4 (2000), no. 3, 553-563

Mathematics

Algebraic Geometry

The proof of Claim 4.3 is corrected and simplified

Scientific paper

Let G be a finite group acting on a symplectic complex vector space V. Assume that the quotient V/G has a holomorphic symplectic resolution. We prove that G is generated by "symplectic reflectionsd"', i.e. symplectomorphisms with fixed space of codimension 2 in V. Symplectic resolutions are always semismall. A crepant resolution of V/G is always symplectic. We give a symplectic version of Nakamura conjectures.

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