Holomorphic structures on 4-folds with first Betti numbers equal to 1
by
Georges Dloussky
Universite d'Aix-Marseille I, France

Oral Communication

These non-kälerian complex surfaces S correspond to the VII-class of Kodaira. When the second Betti number b₂=0, we have Hopf surfaces or Inoue surfaces and the situation is well understood. Therefore the talk is intended to give new results about the case n:=b₂ > 0. All known examples contain embeddings of 3-spheres which do not disconnect the manifold (we shall say a Global Spherical Shell) and admit singular holomorphic foliations. We proove that if S admits a global non-trivial vector field then it contains n rational curves and a GSS.

Vector fields and foliations on compact surfaces of class VII₀, by G.Dloussky and K.Oeljeklaus, Ann. Inst. Fourier, 49 (1999), 1503-1545.

Surfaces de la classe VII₀ admettant un champ de vecteurs. G.Dloussky, K.Oeljeklaus, M.Toma Comment. Math. Helvetici 75 (2000).

Surfaces de la classe VII₀ admettant un champ de vecteurs, II. G.Dloussky, K.Oeljeklaus, M.Toma. Preprint 2000.

Date received: June 29, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafh-37.