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 vectoriels et cycles d'ordre fini sur une variété algébrique non compacte
Filtrable bundles of rank 2 on Hopf surfaces.
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.
Formes de torsion analytique et familles des submersions I
Geometry of twisting cochains
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.
Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper Kähler morphisms.
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.
Holomorphic 2-vector bundles on nonalgebraic 2-tori.
Holomorphic convexity of spaces of analytic cycles
Holomorphic line bundles and divisors on a domain of a Stein manifold
Let be an open set of a Stein manifold of dimension such that for . We prove that is Stein if and only if every topologically trivial holomorphic line bundle on is associated to some Cartier divisor on .
Holomorphic line bundles on a domain of a two-dimensional Stein manifold
Let D be an open subset of a two-dimensional Stein manifold S. Then D is Stein if and only if every holomorphic line bundle L on D is the line bundle associated to some (not necessarily effective) Cartier divisor 𝔡 on D.
Holomorphic Morse Inequalities on Manifolds with Boundary
Let be a compact complex manifold with boundary and let be a high power of a hermitian holomorphic line bundle over When has no boundary, Demailly’s holomorphic Morse inequalities give asymptotic bounds on the dimensions of the Dolbeault cohomology groups with values in in terms of the curvature of We extend Demailly’s inequalities to the case when has a boundary by adding a boundary term expressed as a certain average of the curvature of the line bundle and the Levi curvature of the...
Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces
In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.
Holomorphic sections of line bundles over (H,C)-Groups.
Holomorphic structures in vector bundles over complex surfaces.
Holomorphic Vector Fields and Kaehler Manifolds.
Holomorphic Vector Fields on Complex Surfaces.