Abstract
We present a method to generate many automorphisms of a supersingular K3 surface in odd characteristic. As an application, we show that if p is an odd prime less than or equal to 7919, then every supersingular K3 surface in characteristic p has an automorphism whose characteristic polynomial on the Néron–Severi lattice is a Salem polynomial of degree 22. For a supersingular K3 surface with Artin invariant 10, the same holds for odd primes less than or equal to 17, 389.
Acknowledgments
Thanks are due to Professors Junmyeong Jang, Toshiyuki Katsura, Jonghae Keum, Keiji Oguiso, Matthias Schütt, and Hirokazu Yanagihara for stimulating discussions.
Funding
This work is partially supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (C) No. 25400042.