Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the Saito basis and the Tjurina number for plane branches


Authors: Y. Genzmer and M. E. Hernandes
Journal: Trans. Amer. Math. Soc. 373 (2020), 3693-3707
MSC (2010): Primary 14H50; Secondary 14B05, 32S05
DOI: https://doi.org/10.1090/tran/8019
Published electronically: February 19, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the concept of a good Saito basis for a plane curve and we explore it to obtain a formula for the minimal Tjurina number in a topological class. In particular, we give a lower bound for the Tjurina number in terms of the Milnor number that allows us to present a positive answer to a question of Dimca and Greuel.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14H50, 14B05, 32S05

Retrieve articles in all journals with MSC (2010): 14H50, 14B05, 32S05


Additional Information

Y. Genzmer
Affiliation: Institut de Mathematiques de Toulouse, Université Paul Sabatier, 7-31062 Toulouse, cedex 9, France
Email: yohann.genzmer@math.univ-toulouse.fr

M. E. Hernandes
Affiliation: Departamento de Mathemática, Universidade Estadual de Maringá, Maringá-PR, 87020-900, Brazil
Email: mehernandes@uem.br

DOI: https://doi.org/10.1090/tran/8019
Keywords: Plane curves, Tjurina number, Saito basis
Received by editor(s): April 18, 2019
Received by editor(s) in revised form: September 23, 2019
Published electronically: February 19, 2020
Additional Notes: This work has been partially supported by the Réseau de Coopération France-Brésil.
The second author was also partially supported by CNPq.
Article copyright: © Copyright 2020 American Mathematical Society