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A class of non-algebraic threefolds

Matei Toma (1989)

Annales de l'institut Fourier

Let X be a compact complex nonsingular surface without curves, and E a holomorphic vector bundle of rank 2 on X . It turns out that the associated projective bundle P E has no divisors if and only if E is “strongly” irreducible. Using the results concerning irreducible bundles of [Banica-Le Potier, J. Crelle, 378 (1987), 1-31] and [Elencwajg- Forster, Annales Inst. Fourier, 32-4 (1982), 25-51] we give a proof of existence for bundles which are strongly irreducible.

Bounds of Riesz Transforms on L p Spaces for Second Order Elliptic Operators

Zhongwei Shen (2005)

Annales de l’institut Fourier

Let = -div ( A ( x ) ) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on n or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed p > 2 , a necessary and sufficient condition is obtained for the boundedness of the Riesz transform ( ) - 1 / 2 on the L p space. As an application, for 1 < p < 3 + ϵ , we establish the L p boundedness of Riesz transforms on Lipschitz domains for operators with V M O coefficients. The range of p is sharp. The closely related boundedness of ...

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.

Colmatage de surfaces holomorphes et classification des surfaces compactes

Georges Dloussky (1993)

Annales de l'institut Fourier

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 Σ , 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 Σ donnent des cartes locales. On démontre que dans une...

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