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

Tom 70 / 1998

Georges Dloussky, Franz Kohler Annales Polonici Mathematici 70 (1998), 49-83 DOI: 10.4064/ap-70-1-49-83


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 $b_1=1$ 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.


  • Georges Dloussky
  • Franz Kohler

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