On K3 surfaces with hyperbolic automorphism groups
Algebraic Geometry
2026-05-05 v3 Group Theory
Abstract
We show the finiteness of the N\'eron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number which is optimal to ensure the finiteness. Our proof of finiteness is based on the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu.
Cite
@article{arxiv.2507.13726,
title = {On K3 surfaces with hyperbolic automorphism groups},
author = {Koji Fujiwara and Keiji Oguiso and Xun Yu},
journal= {arXiv preprint arXiv:2507.13726},
year = {2026}
}
Comments
25 pages, final version to appear in Crelle's journal