On the Hilbert function and the minimal free resolution of the GF(q)-points of Del Pezzo surfaces of P^n

Abstract

Here we study the Hilbert function of the points rational over a fixed finite field GF(q), q = pe of some Del Pezzo surfaces and of the Veronese plane. This work is motivated by the equivalence (due to Moorhouse) between the knowledge of the Hilbert function of a finite set of a projective space over GF(q) and the p-rank of its incidence matrix.