A Note on 1-Forms for Reduced Curve Singularities

2017/09/03 by Gert–Martin Greuel, Greuel, Gert-Martin
Mathematics · #13H #14B #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1709.00679

openalex publication_date 2017/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Milnor and Tjurina numbers for a hypersurface germ with isolated singularity

Related

• Homological index for 1-forms and a Milnor number for isolated singularities
• A remark on 1-forms and plane curve singularities
• Holomorphic 1-forms on some coverings of the moduli space of curves
• On the quotient of Milnor and Tjurina numbers for two-dimensional isolated hypersurface singularities
• The Complete Intersection Discrepancy of a Curve II: Families of Curves