The local Poincaré problem for irreducible branches

• José Maria Cano ^[1] ; Pedro Fortuny Ayuso ^[2] ; Javier Ribón ^[3]
  1. [1] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     
  2. [2] Universidad de Oviedo

     Universidad de Oviedo

     Oviedo, España

     
  3. [3] Universidade Federal Fluminense

     Universidade Federal Fluminense

     Brasil

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 6, 2021, págs. 2229-2244
• Idioma: inglés
• DOI: 10.4171/rmi/1260
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.