The Poincaré problem for reducible curves

  1. Pedro Fortuny Ayuso 1
  2. Javier Ribón 2
  1. 1 Universidad de Oviedo
    info
    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

    Geographic location of the organization Universidad de Oviedo
  2. 2 Universidade Federal Fluminense
    info
    Universidade Federal Fluminense

    Niterói, Brasil

    ROR https://ror.org/02rjhbb08

    Geographic location of the organization Universidade Federal Fluminense
Journal:
Revista matemática iberoamericana

ISSN: 0213-2230

Year of publication: 2024

Volume: 40

Issue: 1

Pages: 251-276

Type: Article

DOI: 10.4171/RMI/1451 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista matemática iberoamericana

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Abstract

We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we apply our methods to invariant curves whose branches are isolated, i.e., they are never contained in non-trivial analytic families of equisingular invariant curves. In this case, we show that the multiplicity of an invariant curve is at most twice the multiplicity of the foliation. Finally, we apply the local methods to foliations in the complex projective plane.

Data source: Dialnet