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ArticleOriginal scientific text

Title

Classification of singular germs of mappings and deformations of compact surfaces of class VII₀

Authors 1, 2

Affiliations

  1. U.R.A. 225 C.N.R.S., Centre de Mathématiques et d'Informatique, Université d'Aix-Marseille I, 39, rue F. Joliot-Curie, F-13453 Marseille Cedex 13, France
  2. Département de Mathématiques, Université d'Angers, 2, Bd Lavoisier, F-49045 Angers Cedex, France

Abstract

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 b1=1 and b₂>0 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.

Keywords

ENG
surfaces of class VII₀, germs of mappings

Bibliography

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Annales Polonici Mathematici
1998/70/1
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Pages:
49-83
Main language of publication
English
Received
1997-10-05
Accepted
1998-08-26
Published
1998
Exact and natural sciences