Holomorphic symplectic geometry and orbifold singularities
Algebraic Geometry
2007-05-23 v3 Complex Variables
Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.math/9903175,
title = {Holomorphic symplectic geometry and orbifold singularities},
author = {Misha Verbitsky},
journal= {arXiv preprint arXiv:math/9903175},
year = {2007}
}
Comments
The proof of Claim 4.3 is corrected and simplified