On the Saito basis and the Tjurina number for plane branches
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- by Y. Genzmer and M. E. Hernandes PDF
- Trans. Amer. Math. Soc. 373 (2020), 3693-3707 Request permission
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
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Additional Information
- Y. Genzmer
- Affiliation: Institut de Mathematiques de Toulouse, Université Paul Sabatier, 7-31062 Toulouse, cedex 9, France
- MR Author ID: 803766
- Email: yohann.genzmer@math.univ-toulouse.fr
- M. E. Hernandes
- Affiliation: Departamento de Mathemática, Universidade Estadual de Maringá, Maringá-PR, 87020-900, Brazil
- MR Author ID: 682682
- Email: mehernandes@uem.br
- 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. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 3693-3707
- MSC (2010): Primary 14H50; Secondary 14B05, 32S05
- DOI: https://doi.org/10.1090/tran/8019
- MathSciNet review: 4082253