Free automorphism groups of K3 surfaces with Picard number 3

2023/06/28 by Hashimoto, Kenji, Lee, Kwangwoo · 1 citation
#14J28 #14J50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.16147

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 PSL₂(ℤ). In particular, we show that a free group of arbitrarily large rank appears as the automorphism group of such a K3 surface.

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• Unboundedness of fixed point multiplicities on a K3 surface

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