Generalized Intermediate Jacobians and the Theorem on Normal Functions.
Geometry and cohomology of certain domains in the complex projective space.
Geometry of some twistor spaces of algebraic dimension one
It is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by...
Geometry of the Kepler system in coherent states approach
Geometry of twisting cochains
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....
Harmonic metrics and connections with irregular singularities
We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface with the complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same complex.
Hermitian-Einstein Connections and Stable Vector Bundles Over Compact Complex Surfaces.
Higgs bundles and local systems
Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper Kähler morphisms.
Hilbert spaces for massless particles with nonvanishing helicities
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 convexity of spaces of analytic cycles
Holomorphic Fiber Bundles whose Fibers are Bounded Stein Domains with Zero First Betti Number.
Holomorphic Fibrations of Bounded Domains.