Symplectic automorphisms and the Picard group of a K3 surface
Algebraic Geometry
2010-05-12 v3
Abstract
We consider the symplectic action of a finite group G on a K3 surface. The Picard group of the K3 surface has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then describe moduli spaces of K3 surfaces with symplectic G-action, extending results of Nikulin in the abelian case. We use our moduli spaces to develop techniques for classifying all possible symplectic actions of a group G.
Keywords
Cite
@article{arxiv.0902.0601,
title = {Symplectic automorphisms and the Picard group of a K3 surface},
author = {Ursula Whitcher},
journal= {arXiv preprint arXiv:0902.0601},
year = {2010}
}
Comments
10 pages; improved exposition in Section 3. To appear in Communications in Algebra.