Fundamental groups of symplectic singularities
Algebraic Geometry
2013-04-12 v6
Abstract
Let (X, \omega) be an affine symplectic variety. Assume that X has a C^*-action with positive weights and \omega is homogeneous with respect to the C^*-action. We prove that the algebraic fundamental group of the smooth locus X_{reg} is finite. This is a collorary to a more general theorem: If an affine variety X has a C^*action with positive weights and the log pair (X, 0) has klt singularities, then the algebraic fundamental group of X_{reg} is finite.
Cite
@article{arxiv.1301.1008,
title = {Fundamental groups of symplectic singularities},
author = {Yoshinori Namikawa},
journal= {arXiv preprint arXiv:1301.1008},
year = {2013}
}
Comments
11 pages: For proving the finiteness of algebraic fundamental group, only the klt condition is necessary