The minimal Tjurina number of irreducible germs of plane curve singularities
| Autor: | Alejandro Melle-Hernández, Guillem Blanco, Maria Alberich-Carramiñana, Patricio Almirón |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions, Ministerio de Economía y Competitividad (España), Generalitat de Catalunya |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Class (set theory) Plane curve General Mathematics Commutative Algebra (math.AC) Mathematics - Algebraic Geometry Singularitats (Matemàtica) 14 Algebraic geometry::14H Curves [Classificació AMS] Mathematics::Algebraic Geometry Singularity Tjurina number Milnor number Tjurina number FOS: Mathematics Germ 32 Several complex variables and analytic spaces::32S Singularities [Classificació AMS] Algebraic Geometry (math.AG) Quotient Milnor number Mathematics Sequence Singularities (Mathematics) Matemàtiques i estadística [Àrees temàtiques de la UPC] Mathematics - Commutative Algebra Curves Algebraic Gravitational singularity Curve singularities Corbes algebraiques Resolution (algebra) |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Digital.CSIC. Repositorio Institucional del CSIC instname |
| ISSN: | 0022-2518 |
| DOI: | 10.1512/iumj.2021.70.8583 |
| Popis: | 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 [6], and by Wall and Mattei [11, 13]. The first and third authors were supported by Spanish Ministerio de Ciencia, Innovación y Universidades MTM2015-69135-P, Generalitat de Catalunya 2017SGR-932 projects, and they are with the Barcelona Graduate School of Mathematics (BGSMath), through the project MDM-2014-0445. The second and fourth authors were supported by Spanish Ministerio de Ciencia, Innovación y Universidades MTM2016-76868-C2-1-P |
| Databáze: | OpenAIRE |
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