Treffer: The minimal tjurina number of irreducible germs of plane curve singularities

Title:
The minimal tjurina number of irreducible germs of plane curve singularities
Authors:
Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions, Alberich Carramiñana, Maria, Almirón Cuadros, Patricio, Blanco Fernández, Guillem, Melle Hernández, Alejandro
Publisher Information:
2021-01-01
Document Type:
E-Ressource Electronic Resource
Index Terms:
Àrees temàtiques de la UPC::Matemàtiques i estadística, 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, Article
URL:
https://arxiv.org/abs/1904.02652
http://hdl.handle.net/2117/362685
http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=8583&year=2021&volume=70
Availability:
Open access content. Open access content
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es
Open Access
Note:
10 p.
application/pdf
English
Other Numbers:
HGF oai:upcommons.upc.edu:2117/362685
Alberich, M. [et al.]. The minimal tjurina number of irreducible germs of plane curve singularities. "Indiana University mathematics journal", 1 Gener 2021, vol. 70, p. 1211-1220.
0022-2518
10.1512/IUMJ.2021.70.8583
1298722103
Contributing Source:
UNIV POLITECNICA DE CATALUNYA
From OAIster®, provided by the OCLC Cooperative.
Accession Number:
edsoai.on1298722103
Database:
OAIster

Weitere Informationen

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.
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.
Peer Reviewed
Postprint (author's final draft)