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# Communications in Analysis and Geometry

## Volume 21 (2013)

### Number 3

### Characterization of isolated complete intersection singularities with $\mathbb{C}^*$-action of dimension $n \geq 2$ by means of geometric genus and irregularity

Pages: 509 – 526

DOI: http://dx.doi.org/10.4310/CAG.2013.v21.n3.a2

#### Authors

#### Abstract

Dedicated to Professor Michael Artin on the occasion of his 79th birthday It is well known that geometric genus $p_g$ and irregularity $q$ are two important invariants for isolated singularities. In this paper, we give a formula relating $p_g$ and $q$ for isolated singularities with $\mathbb{C}^*$-action in any dimension. We also give a simple characterization of the quasi-homogeneous isolated complete intersection singularities using $p_g$ and $q$ . As a corollary, we prove that q is an invariant of topological type for two-dimensional weighted homogeneous hypersurface singularities.

Published 5 July 2013