English

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.