Symplectic automorphisms and the Picard group of a K3 surface

Details Symplectic automorphisms and the Picard group of a K3 surface Symplectic automorphisms and the Picard group of a K3 surface

2009-02-03

arxiv.org/abs/0902.0601v3

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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