descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2021Embargo end date: 01 Jan 2019 English Publisher:Indiana University Mathematics JournalJournal:Indiana University Mathematics Journal, volume 70, pages 1,211-1,220 (issn: 0022-2518,

Authors: Alberich Carramiñana, Maria; Almirón Cuadros, Patricio; Blanco Fernández, Guillem; Melle Hernández, Alejandro;

doi: 10.1512/iumj.2021.70.8583 , 10.48550/arxiv.1904.02652

arXiv: 1904.02652

handle: 20.500.14352/7204 , 10261/261278 , 2117/362685

The minimal Tjurina number of irreducible germs of plane curve singularities

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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, Wall and Mattei.

To appear in Indiana University Mathematics Journal. Minor changes. Improvement in Corollary 2

Related Organizations

Universitat Politècnica de Catalunya
Spain
Complutense University of Madrid
Spain
University of Barcelona
Spain
Universitat Polite`cnica de Catalunya
Spain
Spanish National Research Council
Spain

Keywords

Funciones (Matemáticas), Local complex singularities, 1202 Análisis y Análisis Funcional, Singularities of curves, local rings, Commutative Algebra (math.AC), Algebraic, Mathematics - Algebraic Geometry, Singularitats (Matemàtica), :14 Algebraic geometry::14H Curves [Classificació AMS], Classificació AMS::32 Several complex variables and analytic spaces::32S Singularities, Tjurina number, Milnor number, Tjurina number, curve singularities, FOS: Mathematics, :32 Several complex variables and analytic spaces::32S Singularities [Classificació AMS], Algebraic Geometry (math.AG), Curves, Milnor number, Àrees temàtiques de la UPC::Matemàtiques i estadística, Singularities (Mathematics), :Matemàtiques i estadística [Àrees temàtiques de la UPC], Mathematics - Commutative Algebra, Classificació AMS::14 Algebraic geometry::14H Curves, Curves, Algebraic, Plane and space curves, 1201.01 Geometría Algebraica, Geometria algebraica, 512.76/.77, Curve singularities, Corbes algebraiques

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