English

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.

Keywords

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