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From non-Kählerian surfaces to Cremona group of P2(C)

100%

Dloussky G.

Complex Manifolds

2014

tom 1

nr 1

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, there is a non empty open set in the Oeljeklaus-Toma moduli space such that the corresponding surfaces are defined by a contracting germ in Cremona group, in particular admit a birational structure.

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

63%

Dloussky G., Kohler F.

Annales Polonici Mathematici

1998

tom 70

nr 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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Complex Manifolds

2 Dloussky G.

1 Kohler F.

1 2014

1 1998

Wyniki wyszukiwania

From non-Kählerian surfaces to Cremona group of P2(C)

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