On the Néron–Severi lattice of a Delsarte surface

Abstract

We suggest an algorithm computing, in some cases, an explicit generating set for the Néron–Severi lattice of a Delsarte surface. In a few special cases, including those of Fermat surfaces and cyclic Delsarte surfaces that were previously conjectured in the literature, we show that certain “obvious” divisors do generate the lattice. The proof is based on the computation of the Alexander module related to a certain abelian covering.