Del Pezzo surfaces over finite fields

2018/03/17 by Trepalin, Andrey · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1803.07421

Abstract

Let X be a del Pezzo surface of degree 2 or greater over a finite field \mathbbF_q. The image Γ of the Galois group Gal(\mathbbF_q / \mathbbF_q) in the group Aut(Pic(X)) is a cyclic subgroup preserving the anticanonical class and the intersection form. The conjugacy class of Γ in the subgroup of Aut(Pic(X)) preserving the anticanonical class and the intersection form is a natural invariant of X. We say that the conjugacy class of Γ in Aut(Pic(X)) is the type of a del Pezzo surface. In this paper we study which types of del Pezzo surfaces of degree 2 or greater can be realized for given q. We collect known results about this problem and fill the gaps.

Cited by

• Automorphisms of del Pezzo surfaces without points

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