Contact geometry and complex surfaces.
Convex bodies and algebraic geometry [Book]
Convexity on the space of Kähler metrics
These are the lecture notes of a minicourse given at a winter school in Marseille 2011. The aim of the course was to give an introduction to recent work on the geometry of the space of Kähler metrics associated to an ample line bundle. The emphasis of the course was the role of convexity, both as a motivating example and as a tool.
Coréduction algébrique d'un espace analytique faiblement Kählérien compact.
Courants kählériens et surfaces compactes
Le théorème de régularisation de Demailly ramène l’existence d’une métrique kählérienne sur une surface compacte à celle d’un (1-1)-courant strictement positif -fermé (“courant kählérien”). Après avoir démontré un critère d’existence d’un tel courant, nous utilisons la symétrie de Hodge pour donner une démonstration unifiée du caractère kählérien des surfaces compactes à premier nombre de Betti pair.
Covering spaces of an elliptic surface
Criteria for Quasi-Projectivity.
Decomposition of Compact Complex Varieties and the Cancellation Problem.
Deformation of Complete Intersections with Singularities.
Deformation of Varieties Defined by Sections in Homogeneous Vector Bundles.
Deformation rigidity of the rational homogeneous space associated to a long simple root
Deformations of coherent foliations on a compact normal space
An universal analytic structure is construted on the set of (singular) holomorphic foliations on a normal compact space. Such a foliation is by definition a coherent subsheaf of the holomorphic tangent sheaf stable by the Lie-bracket
Deformations of Kähler manifolds with nonvanishing holomorphic vector fields
We study compact Kähler manifolds admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of . We extend Calabi’s theorem on the structure of compact Kähler...
Der Kodairasche Verschwindungssatz auf streng pseudokonvexen Räumen. I.
Der Satz von Kuranishi für kompakte komplexe Räume.
Diastatic entropy and rigidity of complex hyperbolic manifolds
Let f : Y → X be a continuous map between a compact real analytic Kähler manifold (Y, g) and a compact complex hyperbolic manifold (X, g0). In this paper we give a lower bound of the diastatic entropy of (Y, g) in terms of the diastatic entropy of (X, g0) and the degree of f . When the lower bound is attained we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G. Courtois and S. Gallot [2] for the volume entropy. As a corollary,when X = Y,we...
Diffeomorphisms of a K3 Surface.
Divisorial Zariski decompositions on compact complex manifolds
Ein allgemeines Kriterium für das formale Prinzip.
Ein Endlichkeitssatz für Hyperflächen auf kompakten komplexen Räumen.