The most symmetric smooth cubic surface over a finite field of characteristic $2$

Abstract

In this paper we find the largest automorphism group of a smooth cubic surface over any finite field of characteristic $2.$ We prove that if the order of the field is a power of $4,$ then the automorphism group of maximal order of~a~smooth cubic surface over this field is ${\mathrm{PSU}}_4({\mathbb{F}}_2).$ If the order of the field of characteristic $2$ is not a power of $4,$ then we prove that the automorphism group of maximal order of a smooth cubic surface over this field is the symmetric group of degree $6.$ Moreover, we prove that smooth cubic surfaces with such properties are unique up to isomorphism.

References in corpus (1)

• Jordan constant for Cremona group of rank 2 over a finite field

Cited by in corpus (1)

• The most symmetric smooth cubic surface