Minimal del Pezzo surfaces of degree 2 over finite fields

摘要

Let X be a minimal del Pezzo surface of degree 2 over afinite field Fq. The image Γ of the Galois group Gal(Fq/Fq) in the groupAut(Pic(X)) is a cyclic subgroup of the Weyl group W(E7). There are 60conjugacy classes of cyclic subgroups in W(E7) and 18 of them correspondto minimal del Pezzo surfaces. In this paper we study which possibilitiesof these subgroups for minimal del Pezzo surfaces of degree 2 can beachieved for given q.