Automorphisms of Supersingular K3 Surfaces and Salem Polynomials

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.

Keywords:

• supersingular K3 surface
• automorphism
• Salem polynomial

2000 AMS Subject Classification:

• 14J28
• 14J50
• 37B40
• 14Q10

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.