On K3 surfaces with hyperbolic automorphism groups

Work of Xun Yu

Joint with Koji Fujiwara and Keiji Oguiso

Since the global Torelli theorem for K3 surfaces by Piatetskii-Shapiro and Shafarevich, the automorphism groups of K3 surfaces have caught much attention from several aspects by several mathematicians. In this paper, inspired by recent work of Kikuta and Takatsu, we address a new study of the automorphism group of a K3 surface from hyperbolicity in geometric group theory. We show the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the (optimal) assumption that the Picard number is greater than or equal to 6.

J. Reine Angew. Math.

https://doi.org/10.48550/arXiv.2507.13726