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Let S be a smooth simply-connected complex projective surface, and let A be a finite abelian group. We define invariants TA, FA and σA 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.

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