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. 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.

10 pages; improved exposition in Section 3. To appear in Communications in Algebra.

References in corpus (6)

• Picard-Fuchs Differential Equations for Families of K3 Surfaces
• Period map of a certain K3 family with an S5-action
• Algebraic K-theory of toric hypersurfaces
• Orbifoldes à premi\ere classe de Chern nulle
• The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces
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Cited by in corpus (1)

• The dihedral group $\Dh_5$ as group of symplectic automorphisms on K3 surfaces