Isolated invariant curves of a foliation

Nuria Corral; Percy Fernández-Sánchez

Isolated invariant curves of a foliation

Nuria Corral, Percy Fernández-Sánchez

Sección de Matemáticas

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation F of (ℂ2,0) in terms of the Milnor number of F. This result gives a bound for the degree of an algebraic invariant curve C ⊂ ℙℂ2 of a foliation G of ℙℂ2 in terms of the degree of G, provided that all the branches of C are isolated separatrices. ©2005 American Mathematical Society.

Original language	Spanish
Pages (from-to)	1125-1132
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	134
State	Published - 1 Jan 2006

Cite this

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title = "Isolated invariant curves of a foliation",

abstract = "We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation F of (ℂ2,0) in terms of the Milnor number of F. This result gives a bound for the degree of an algebraic invariant curve C ⊂ ℙℂ2 of a foliation G of ℙℂ2 in terms of the degree of G, provided that all the branches of C are isolated separatrices. {\textcopyright}2005 American Mathematical Society.",

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AU - Fernández-Sánchez, Percy

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N2 - We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation F of (ℂ2,0) in terms of the Milnor number of F. This result gives a bound for the degree of an algebraic invariant curve C ⊂ ℙℂ2 of a foliation G of ℙℂ2 in terms of the degree of G, provided that all the branches of C are isolated separatrices. ©2005 American Mathematical Society.

AB - We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation F of (ℂ2,0) in terms of the Milnor number of F. This result gives a bound for the degree of an algebraic invariant curve C ⊂ ℙℂ2 of a foliation G of ℙℂ2 in terms of the degree of G, provided that all the branches of C are isolated separatrices. ©2005 American Mathematical Society.

M3 - Artículo

SN - 0002-9939

VL - 134

SP - 1125

EP - 1132

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -