This work studies abelian branched coverings of smooth complex projective surfaces from the topological viewpoint. Geometric information about the coverings (such as the first Betti numbers of a smooth model or intersections of embedded curves) is related to topological and combinatorial information about the base space and branch locus. Special attention is given to examples in which the base space is the complex projective plane and the branch locus is a configuration of lines.

Readership

Graduate students and researchers.

Table of Contents

• Introduction
• Preliminaries
• Intersections of curves on covering surfaces
• Hirzebruch covering surfaces
• Algorithm for computing the first Betti number
• Examples
• References