Sur les feuilletages holomorphes singuliers de codimension 1

• Autores: Bouchra Gmira
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 1, 1992, págs. 229-240
• Idioma: francés
• Títulos paralelos:
  • Sobre foliaciones holomorfas singulares de codimensión 1
  • On codimension-one singular holomorphic foliations
• Enlaces
  • Texto completo
• Resumen

  • Let F be a codimension one holomorphic foliation whose singular set S is contained in a compact leaf S of F.

    When F is of dimension one, S 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 S is of any dimension m, we can define a such index ia along the maximal dimension strates {Sa} of a suitable stratification of the complex variety S. Let sa be the fundamental cycle of Sa, s the 2m-cycle of S defined by s = Sia.sa and s* the 2-cocycle dual to s by Poincaré isomorphism H2(S) ? H2m(S), we prove that the cohomology class [s*] equals the Euler class c1(E).