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

Georges Dloussky, Franz Kohler (1998)

Annales Polonici Mathematici

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 b > 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.

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