Theta functions on -bundles over with the zero Euler class.
Theta functions on the Kodaira-Thurston manifold.
Three-manifolds and Kähler groups
We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is or .
Torelli theorems for Kähler K3 surfaces
Un complément à l’article de Dloussky sur le colmatage des surfaces holomorphes
Nous étudions les surfaces complexes compactes qui sont des dégénérations de surfaces de Hopf éclatées. Nous démontrons que si une telle surface contient une hypersurface réelle globale strictement pseudoconvexe, alors est une surface de Kato. Ceci permet d’améliorer un résultat de Dloussky, paru dans ce même journal en 1993.
Une caractérisation des surfaces d'Inoue-Hirzebruch
On montre que parmi les surfaces compactes complexes de classe avec , les surfaces d’Inoue-Hirzebruch sont caractérisées par le fait qu’elles possèdent deux champs de vecteurs tordus. Ce résultat est un pas vers la compréhension des feuilletages sur les surfaces .
Vector bundles on blown-up Hopf surfaces
We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These are the moduli spaces used by Andrei Teleman in his work on the classification of class VII surfaces.
Vector bundles on non-Kaehler elliptic principal bundles
We study relatively semi-stable vector bundles and their moduli on non-Kähler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-Kähler elliptic principal bundle over a primary Kodaira surface are computed.
Vector fields and foliations on compact surfaces of class
It is well-known that minimal compact complex surfaces with containing global spherical shells are in the class VII of Kodaira. In fact, there are no other known examples. In this paper we prove that all surfaces with global spherical shells admit a singular holomorphic foliation. The existence of a numerically anticanonical divisor is a necessary condition for the existence of a global holomorphic vector field. Conversely, given the existence of a numerically anticanonical divisor, surfaces...
Weierstraß-Punkte und kanonische Familien von Riemannschen Metriken auf regulären Familien kompakter Riemannscher Flächen (II).
Zur Klassifikation glatter kompakter C*-Flächen.
О гиперболической вложенности дополнений к дивизорам и предельном поведении метрики Кобаяси-Ройдена