Free automorphism groups of K3 surfaces with Picard number 3

Abstract

It is known that the automorphism group of any projective K3 surface is finitely generated [24]. In this paper, we consider a certain kind of K3 surfaces with Picard number 3 whose automorphism groups are isomorphic to congruence subgroups of the modular group $PS{L}_2(\mathbb{Z})$. In particular, we show that a free group of arbitrarily large rank appears as the automorphism group of such a K3 surface.

34 pages; added Sections 8.2 and 9; comments are welcome