Publication

The minimal Tjurina number of irreducible germs of plane curve singularities

Journal Article (2021)

Journal

Indiana University Mathematics Journal

Pages

1211-1220

Volume

70

Number

4

Doc link

http://dx.doi.org/10.1512/IUMJ.2021.70.8583

File

Download the digital copy of the doc pdf document

Authors

Abstract

In this paper we give a positive answer to a question of Dimca and Greuel about the quotient between the Milnor and the Tjurina numbers for any irreducible germ of plane curve singularity. This result is based on a closed formula for the minimal Tjurina number of an equisingularity class in terms of the sequence of multiplicities of the strict transform along a resolution. The key points for the proof are previous results by Genzmer, and by Wall and Mattei.

Categories

pattern recognition.

Author keywords

Curve singularities; Tjurina number; Milnor number

Scientific reference

M. Alberich-Carramiñana, P. Almirón, G. Blanco and A. Melle-Hernández. The minimal Tjurina number of irreducible germs of plane curve singularities. Indiana University Mathematics Journal, 70(4): 1211-1220, 2021.