Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2023; 60(6): 1427-1437

Online first article November 16, 2023      Printed November 30, 2023

https://doi.org/10.4134/BKMS.b220371

Copyright © The Korean Mathematical Society.

Automorphisms of K3 surfaces with Picard number two

Kwangwoo Lee

Chungnam National University

Abstract

It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.

Keywords: K3 surface, automorphism, Pell equation

MSC numbers: Primary 14J28, 14J50

Supported by: The author was supported by National Research Foundation of Korea(NRF-2020R1 I1A1A01073662) and National Research Foundation of Korea(NRF-2021R1A4A3033098) grant funded by the Korea government(MSIT).