On the Saito basis and the Tjurina number for plane branches

Yohann Genzmer (1) , M.E. Hernandes (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UEM - Universidade Estadual de Maringá [Brasil] = State University of Maringá [Brazil] = Université d'État de Maringá [Brésil]

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 allow us to present a positive answer for a question of Dimca and Greuel.

Mots clés: Plane curves; Tjurina number; Saito basis

Domaines: Variables complexes [math.CV]; Systèmes dynamiques [math.DS]

Yohann Genzmer, M.E. Hernandes. On the Saito basis and the Tjurina number for plane branches. Transactions of the American Mathematical Society, 2020, 373 (5), pp.3693-3707. ⟨10.1090/tran/8019⟩. ⟨hal-03794511⟩