Topology of curves on a surface and lattice-theoretic invariants of coverings of the surface

Abstract

Let $S$ be a smooth simply-connected complex projective surface, and let $A$ be a finite abelian group. We define invariants $T_A$, $F_A$ and $\sigma_A$ for curves $B$ on $S$ by means of étale Galois coverings of the complement of $B$ with the Galois group $A$, and show that they are useful in finding examples of Zariski pairs of curves on $S$. We also investigate the relation between these invariants and the fundamental group of the complement of $B$.