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Classes de cohomologie positives dans les variétés kählériennes compactes

Olivier Debarre (2004/2005)

Séminaire Bourbaki

Étant donnée une variété kählérienne compacte X , on étudie dans l’espace vectoriel réel de cohomologie de Dolbeault H 1 , 1 ( X , 𝐑 ) H 2 ( X , 𝐑 ) le cône convexe des classes de Kähler ainsi que celui, plus grand, des classes de courants positifs fermés de type ( 1 , 1 ) . Lorsque X est projective, les traces de ces cônes sur l’espace de Néron–Severi NS ( X ) 𝐑 H 1 , 1 ( X , 𝐑 ) engendré par les classes entières sont respectivement le cône des classes de diviseurs amples et l’adhérence de celui des classes de diviseurs effectifs.

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...

Compact Kähler manifolds with compactifiable universal cover

Benoît Claudon, Andreas Höring (2013)

Bulletin de la Société Mathématique de France

In this appendix, we observe that Iitaka’s conjecture fits in the more general context of special manifolds, in which the relevant statements follow from the particular cases of projective and simple manifolds.

Compact lcK manifolds with parallel vector fields

Andrei Moroianu (2015)

Complex Manifolds

We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.

Compact quotients of large domains in complex projective space

Finnur Lárusson (1998)

Annales de l'institut Fourier

We study compact complex manifolds covered by a domain in n -dimensional projective space whose complement E is non-empty with ( 2 n - 2 ) -dimensional Hausdorff measure zero. Such manifolds only exist for n 3 . They do not belong to the class 𝒞 , so they are neither Kähler nor Moishezon, their Kodaira dimension is - , their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which...

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