A Note on 1-Forms for Reduced Curve Singularities

TL;DR

This paper reviews classical results on holomorphic 1-forms for reduced complex curve singularities, especially complete intersections, and compares key invariants like Milnor and Tjurina numbers.

Contribution

It provides a comparative analysis of invariants associated with holomorphic 1-forms in reduced curve singularities, highlighting their relationships.

Findings

Milnor number and Tjurina number comparison

Dimension analysis of torsion part of 1-forms

Results specific to complete intersection singularities

Abstract

We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity, in particular of a complete intersection, and use them to compare the Milnor number, the Tjurina number and the dimension of the torsion part of the 1-forms.