The minimal Tjurina number of irreducible germs of plane curve\n singularities

2019/04/04 by Maria Alberich‐Carramiñana, Alberich-Carramiñana, Maria, Patricio Almirón +5
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1904.02652

openalex publication_date 2019/04/04 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

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

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