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The local Poincaré problem for irreducible branches.
- Source :
- Revista Mathematica Iberoamericana; 2021, Vol. 37 Issue 6, p2229-2244, 16p
- Publication Year :
- 2021
-
Abstract
- Let F be a germ of holomorphic foliation defined in a neighborhood of the origin of C° 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- MULTIPLICITY (Mathematics)
NEIGHBORHOODS
MICROORGANISMS
FOLIATIONS (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 02132230
- Volume :
- 37
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Revista Mathematica Iberoamericana
- Publication Type :
- Academic Journal
- Accession number :
- 152338207
- Full Text :
- https://doi.org/10.4171/rmi/1260