Fibrés stables et métriques d'Hermite-Einstein
Fibrés uniformes de rang élevé sur
Un fibré vectoriel holomorphe sur est dit uniforme si ses images réciproques sous tous les plongements linéaires sont isomorphes. Nous classons les fibrés uniformes de rang 4 sur .
Fibrés uniformes de type (0, . . . , 0, - 1, . . ., -1) sur P2.
Fibrés vectoriels holomorphes homogènes et J-représentations
Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans torsion
On généralise dans cet article la notion de filtration de Harder-Narasimhan au cas des fibrés complexes sur une variété presque complexe compacte d'une part, et au cas des faisceaux cohérents sans torsion sur une variété holomorphe d'autre part. On démontre, dans les deux cas, l'existence d'un déstabilisant maximal. On obtient un théorème de convergence en famille et par là-même l'ouverture de la stabilité en déformation.
Finsler Structures of Negative Curvature in ...-Linear Fibre Spaces.
Generalized Intermediate Jacobians and the Theorem on Normal Functions.
Geometry of universal embedding spaces for almost complex manifolds
We investigate the geometry of universal embedding spaces for compact almost-complex manifolds of a given dimension, and related constructions that allow for an extrinsic study of the integrability of almost-complex structures. These embedding spaces were introduced by J-P. Demailly and H. Gaussier, and are complex algebraic analogues of twistor spaces. Their goal was to study a conjecture made by F. Bogomolov asserting the “transverse embeddability” of arbitrary compact complex manifolds into foliated...
Groupes de cohomologie d'un fibré holomorphe à base et à fibre de Stein.
Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
We give here a generalization of the theory of optimal destabilizing 1-parameter subgroups to non algebraic complex geometry : we consider holomorphic actions of a complex reductive Lie group on a finite dimensional (possibly non compact) Kähler manifold. In a second part we show how these results may extend in the gauge theoretical framework and we discuss the relation between the Harder-Narasimhan filtration and the optimal detstabilizing vectors of a non semistable object....
Higgs bundles and local systems
Hodge metrics and the curvature of higher direct images
Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.
Holomorphe Vektorbündel auf Pn mit c1 = 0 und c2 = 1.
Holomorphic 2-vector bundles on nonalgebraic 2-tori.
Holomorphic Conformal Structures and Uniformization of Complex Surfaces.
Holomorphic Fiber Bundles whose Fibers are Bounded Stein Domains with Zero First Betti Number.
Holomorphic Fibrations of Bounded Domains.
Holomorphic flows and complex structures on products of odd dimensional spheres.
Holomorphic framings for projections in a Banach algebra.
Holomorphic Lagrangian bundles over flag manifolds.