Structure des surfaces de Kato
From non-Kählerian surfaces to Cremona group of P 2 (C)
For any minimal compact complex surface S with n = b2(S) > 0 containing global spherical shells (GSS) we study the effectiveness of the 2n parameters given by the n blown up points. There exists a family of surfaces S → B with GSS which contains as fibers S, some Inoue-Hirzebruch surface and non minimal surfaces, such that blown up points are generically effective parameters. These families are versal outside a non empty hypersurface T ⊂ B. We deduce that, for any configuration of rational curves,...
Colmatage de surfaces holomorphes et classification des surfaces compactes
On considère le problème du colmatage en dimension 2, où l’on examine sous quelle condition une hypersurface strictement pseudoconvexe dans une surface holomorphe est le bord d’un espace de Stein. On montre que l’exemple de Rossi d’une hypersurface strictement pseudoconvexe , qui est le bord de deux domaines non relativement compacts, n’est jamais le bord d’un espace de Stein bien que les fonctions holomorphes définies dans un voisinage de donnent des cartes locales. On démontre que dans une...
Quadratic forms and singularities of genus one or two
We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be -Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing...
Classification of singular germs of mappings and deformations of compact surfaces of class VII₀
We classify generic germs of contracting holomorphic mappings which factorize through blowing-ups, under the relation of conjugation by invertible germs of mappings. As for Hopf surfaces, this is the key to the study of compact complex surfaces with and which contain a global spherical shell. We study automorphisms and deformations and we show that these generic surfaces are endowed with a holomorphic foliation which is unique and stable under any deformation.
Vector fields and foliations on compact surfaces of class
It is well-known that minimal compact complex surfaces with containing are in the class VII of Kodaira. In fact, there are no other known examples. In this paper we prove that all surfaces with global spherical shells admit a singular holomorphic foliation. The existence of a numerically anticanonical divisor is a necessary condition for the existence of a global holomorphic vector field. Conversely, given the existence of a numerically anticanonical divisor, surfaces with a global vector field...
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