Seiberg-Witten invariants and surface singularities II. Singularities with good $\C^*$-action

Abstract

This is a continuation of our paper math.AG/0111298. We prove an explicit formula for the geometric genus p_g of a quasihomogeneous isolated surface singularity in terms of the Seiberg-Witten invariant of the link and other topological data which can be read from a resolution graph of the singularity. Moreover, we also determine all the Reidemeister-Turaev sign-refined torsion of the link (associated with any spin^c structure) in terms of the Seifert invariants.