The local Poincaré problem for irreducible branches

  1. José Maria Cano 1
  2. Pedro Fortuny Ayuso 2
  3. Javier Ribón 3
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

  2. 2 Universidad de Oviedo, Gijón
  3. 3 Universidade Federal Fluminense, Niterói
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Journal:
Revista matemática iberoamericana

ISSN: 0213-2230

Year of publication: 2021

Volume: 37

Issue: 6

Pages: 2229-2244

Type: Article

DOI: 10.4171/RMI/1260 DIALNET GOOGLE SCHOLAR

More publications in: Revista matemática iberoamericana

Abstract

Let F be a germ of holomorphic foliation defined in a neighborhood of the origin of C2 that has a germ of irreducible holomorphic invariant curve γ. We provide a lower bound for the vanishing multiplicity of F at the origin in terms of the equisingularity class of γ. Moreover, we show that such a lower bound is sharp. Finally, we characterize the types of dicritical singularities for which the multiplicity of F can be bounded in terms of that of γ, and provide an explicit bound in this case.

Data source: Dialnet