Cyclic coverings of rational normal surfaces which are quotients of a product of curves

Abstract

This paper deals with cyclic covers of a large family of rational normal surfaces that can also be described as quotients of a product, where the factors are cyclic covers of algebraic curves. We use a generalization of Esnault-Viehweg method to show that the action of the monodromy on the first Betti group of the covering (and its Hodge structure) splits as a direct sum of the same data for some specific cyclic covers over $\mathbb{P}^1$. This has applications to the study of L\^e-Yomdin surface singularities, in particular to the action of the monodromy on the Mixed Hodge Structure, as well as to isotrivial fibered surfaces.