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...

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Detalhes bibliográficos
Autores: Alberich-Carramiñana, Maria, Almirón Patricio, Blanco Fernández, Guillem, Melle-Hernández, Alejandro
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2021
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositório:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/261278
Acesso em linha:http://hdl.handle.net/10261/261278
Access Level:Acceso aberto
Palavra-chave:Curve singularities
Tjurina number, Milnor number
Descrição
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 [6], and by Wall and Mattei [11, 13].