The minimal tjurina number of irreducible germs of plane curve singularities
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...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/362685 |
| Acesso em linha: | https://hdl.handle.net/2117/362685 https://dx.doi.org/10.1512/IUMJ.2021.70.8583 |
| Access Level: | acceso abierto |
| Palavra-chave: | Singularities (Mathematics) Curves, Algebraic Curve singularities Tjurina number Milnor number Singularitats (Matemàtica) Corbes algebraiques Classificació AMS::14 Algebraic geometry::14H Curves Classificació AMS::32 Several complex variables and analytic spaces::32S Singularities Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | 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. |
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