Picard numbers of quintic surfaces

Abstract

We solve the Picard number problem for complex quintic surfaces by proving that every number between 1 and 45 occurs as Picard number of a quintic surface over the rationals. Our main technique consists in arithmetic deformations of Delsarte surfaces, but we also use K3 surfaces and wild automorphisms.

56 pages, 1 figure; v2: minor changes

References in corpus (1)

• The Tate conjecture for K3 surfaces over finite fields

Cited by in corpus (1)

• Effective obstruction to lifting Tate classes from positive characteristic