On codimension-one singular holomorphic foliations.

Bouchra Gmira

Publicacions Matemàtiques (1992)

  • Volume: 36, Issue: 1, page 229-240
  • ISSN: 0214-1493

Abstract

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Let F be a codimension one holomorphic foliation whose singular set Σ is contained in a compact leaf S of F.When F is of dimension one, Σ is a set of isolated points {q1, ..., qr}, C. Camacho and P. Sad define the index of F at each point qk and prove that the sum of these indices equals the Euler class c1(E) of the fibre bundle E normal to S.Generally, whenever Σ is of any dimension m, we can define a such index iα along the maximal dimension strates {Σα} of a suitable stratification of the complex variety Σ. Let σα be the fundamental cycle of Σα, σ the 2m-cycle of S defined by σ = Σiα.σα and σ* the 2-cocycle dual to σ by Poincaré isomorphism H2(S) → H2m(S), we prove that the cohomology class [σ*] equals the Euler class c1(E).

How to cite

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Gmira, Bouchra. "Sur les feuilletages holomorphes singuliers de codimension 1.." Publicacions Matemàtiques 36.1 (1992): 229-240. <http://eudml.org/doc/41154>.

@article{Gmira1992,
author = {Gmira, Bouchra},
journal = {Publicacions Matemàtiques},
keywords = {Foliaciones; Variedades complejas; Variedades analíticas; Holomorfía en varias variables; Isomorfismo; holomorphic foliation; compact leaf; cohomology class; Euler class},
language = {fre},
number = {1},
pages = {229-240},
title = {Sur les feuilletages holomorphes singuliers de codimension 1.},
url = {http://eudml.org/doc/41154},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Gmira, Bouchra
TI - Sur les feuilletages holomorphes singuliers de codimension 1.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 1
SP - 229
EP - 240
LA - fre
KW - Foliaciones; Variedades complejas; Variedades analíticas; Holomorfía en varias variables; Isomorfismo; holomorphic foliation; compact leaf; cohomology class; Euler class
UR - http://eudml.org/doc/41154
ER -

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