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
Authors
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Alberich Carramiñana, Maria
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Almirón, Patricio
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Blanco, Guillem
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Melle-Hernández, Alejandro
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.
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