Coverings of rational ruled normal surfaces

TL;DR

This paper computes the cohomology of Weil divisors on rational ruled toric surfaces using various techniques, and applies these results to analyze the topology of cyclic coverings ramified along certain divisors.

Contribution

It introduces a method to compute cohomology of Weil divisors on rational ruled toric surfaces and studies their cyclic coverings' topology.

Findings

Cohomology formulas for Weil divisors on these surfaces.

Topological properties of cyclic coverings ramified along Q-normal crossing divisors.

New insights into the structure of rational ruled toric surfaces.

Abstract

In this work we use arithmetic, geometric, and combinatorial techniques to compute the cohomology of Weil divisors of a special class of normal surfaces, the so-called rational ruled toric surfaces. These computations are used to study the topology of cyclic coverings of such surfaces ramified along Q-normal crossing divisors.