Resumen de Sur les feuilletages holomorphes singuliers de codimension 1

Bouchra Gmira

• 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).