Frobenius actions on Del Pezzo surfaces of degree 2

Abstract

We determine the number of Del Pezzo surfaces of degree 2 over finite fields of odd characteristic with specified action of the Frobenius endomorphism, i.e. we solve the "quantitative inverse Galois problem". As applications we determine the number of Del Pezzo surfaces of degree 2 with a given number of points and recover results of Banwait-Fité-Loughran and Loughran-Trepalin.

9 pages, 2 tables, comments welcome

References in corpus (4)

• Del Pezzo surfaces over finite fields and their Frobenius traces
• Equivariant cohomology of moduli spaces of genus three curves with level two structure
• Counting Arcs in Projective Planes via Glynn's Algorithm
• Equivariant Cohomology of the Moduli Space of Genus Three Curves with Symplectic Level Two Structure via Point Counts