Symplectic Automorphisms and the Picard Group of a K3 Surface

Abstract

We consider the symplectic action of a finite group G on a K3 surface X. The Picard group of X has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then investigate the classification of symplectic actions by a fixed finite group, using moduli spaces of K3 surfaces with symplectic G-action.

Key Words:

• Algebraic geometry
• Complex surfaces
• K3 surfaces
• Moduli spaces

2000 Mathematics Subject Classification:

• 12J28

ACKNOWLEDGMENT

I thank the referee for comments which improved the exposition of the paper, Alice Garbagnati, Paul Hacking, and Kenji Hashimoto for useful discussion, Charles Doran for his generous guidance, and the organizers of the 2007 GAeL conference in Istanbul, where I presented an early version of this work, for their support.

Notes

Communicated by C. Pedrini.