The Poincaré problem for reducible curves

  1. Pedro Fortuny Ayuso 1
  2. Javier Ribón 2
  1. 1 Universidad de Oviedo, Spain
  2. 2 Universidade Federal Fluminense, Niterói, Brazil
Zeitschrift:
Revista matemática iberoamericana

ISSN: 0213-2230

Datum der Publikation: 2024

Ausgabe: 40

Nummer: 1

Seiten: 251-276

Art: Artikel

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

Andere Publikationen in: Revista matemática iberoamericana

Zusammenfassung

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.

Fuente de los datos: Dialnet