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Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry

Laurent Bruasse, Andrei Teleman (2005)

Annales de l’institut Fourier

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

Carlos T. Simpson (1992)

Publications Mathématiques de l'IHÉS

Hodge metrics and the curvature of higher direct images

Christophe Mourougane, Shigeharu Takayama (2008)

Annales scientifiques de l'École Normale Supérieure

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.

Heinz Spindler (1983)

Manuscripta mathematica

Holomorphic 2-vector bundles on nonalgebraic 2-tori.

Vasile Brinzanescu, Paul Flondor (1985)

Journal für die reine und angewandte Mathematik

Holomorphic Conformal Structures and Uniformization of Complex Surfaces.

Isao Naruki, Ryoichi Kobayashi (1987/1988)

Mathematische Annalen

Holomorphic Fiber Bundles whose Fibers are Bounded Stein Domains with Zero First Betti Number.

Yum-Tong Siu (1976)

Mathematische Annalen

Holomorphic Fibrations of Bounded Domains.

Alan Huckleberry (1977)

Mathematische Annalen

Holomorphic flows and complex structures on products of odd dimensional spheres.

Jean Jaques Loeb, Marcel Nicolau (1996)

Mathematische Annalen

Holomorphic framings for projections in a Banach algebra.

Dupré, Maurice, Glazebrook, James F. (2002)

Georgian Mathematical Journal

Holomorphic Lagrangian bundles over flag manifolds.

Wojciech Bisiecki (1985)

Journal für die reine und angewandte Mathematik

Holomorphic non-holonomic differential systems on complex manifolds

S. Dimiev (1991)

Annales Polonici Mathematici

We study coherent subsheaves 𝓓 of the holomorphic tangent sheaf of a complex manifold. A description of the corresponding 𝓓-stable ideals and their closed complex subspaces is sketched. Our study of non-holonomicity is based on the Noetherian property of coherent analytic sheaves. This is inspired by the paper [3] which is related with some problems of mechanics.

Holomorphic vector bundles on $ℙ_{n}$

Michael Schneider (1978/1979)

Séminaire Bourbaki

Hypersurfaces intégrales des feuilletages holomorphes

Felipe Cano, Jean-François Mattei (1992)

Annales de l'institut Fourier

Soit $ω$ un germe en $0 \in C^{n}$ de 1-forme différentielle holomorphe, satisfaisant la condition d’intégrabilité $ω \land d ω = 0$ et non dicritique, i.e. sur toute surface $Z$ non intégrale de $ω$ , on ne peut tracer, au voisinage de 0, qu’un nombre fini de germes de courbes analytiques $(Γ_{i}, P_{i})$ , intégrales de $ω$ , avec $P_{i} \in Z \cap Sing ω$ . Alors $ω$ possède un germe d’hypersurface analytique intégrale.

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