On the quotient of Milnor and Tjurina numbers for two-dimensional isolated hypersurface singularities

TL;DR

This paper thoroughly investigates the relationship between Milnor and Tjurina numbers in two-dimensional isolated hypersurface singularities, providing a comprehensive answer to a previously posed question and connecting it to broader singularity theory issues.

Contribution

It offers a complete solution to the question about the quotient of Milnor and Tjurina numbers for plane curve singularities and links this to the study of isolated complete intersection singularities.

Findings

Provides a full characterization of the quotient for plane curve singularities.

Establishes connections with broader problems in singularity theory.

Offers new insights into the difference between Milnor and Tjurina numbers.

Abstract

In this paper we give a complete answer to a question posed by Dimca and Greuel about the quotient of the Milnor and Tjurina numbers of a plane curve singularity. We put this question into a general framework of the study of the difference of Milnor and Tjurina numbers for isolated complete intersection singularities showing its connection with other problems in singularity theory.