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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....

Higher-Dimensional Analogues of Inoue-Hirzebruch Surfaces.

G.K. Sankaran (1986)

Mathematische Annalen

Hilbert's Fourteenth Problem for Non-Reductive Groups.

Frank D. Grosshans (1986)

Mathematische Zeitschrift

Hodge groups of K3 surfaces.

Yu.G. Zarhin (1983)

Journal für die reine und angewandte Mathematik

Holomorphic equivariant cohomology.

Kefeng Liu (1995)

Mathematische Annalen

Homogeneous Complex Surfaces.

Karl Oeljeklaus, Wolfgang Richthofer (1984)

Mathematische Annalen

Homogeneous polynomials with isomorphic Milnor algebras

Imran Ahmed (2010)

Czechoslovak Mathematical Journal

We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.

Homogeneous varieties for semisimple groups of rank one

Friedrich Knop (1995)

Compositio Mathematica

Homological dimension of algebras of invariants.

V.L. Popov (1983)

Journal für die reine und angewandte Mathematik

Homology of the Steinberg variety and Weyl group coinvariants.

Douglass, J.M., Röhrle, G. (2009)

Documenta Mathematica

Hyperdéterminant d’un $S L_{2}$ -homomorphisme

Jean Vallès (2008)

Annales mathématiques Blaise Pascal

Etant donnés $A_{1}, \dots, A_{s}$ ( $s \geq 3$ ) des $S L_{2} (ℂ)$ -modules non triviaux de dimensions respectives $n_{1} + 1 \geq \dots \geq n_{s} + 1$ (avec $n_{1} = n_{2} + \dots + n_{s}$ ) et $φ \in ℒ (A_{2} \otimes \dots \otimes A_{s}, A_{1}^{*})$ un $S L_{2} (ℂ)$ -homomorphisme, nous montrons que l’hyperdéterminant de $φ$ est nul sauf si les modules $A_{i}$ sont irréductibles et si l’homomorphisme est la multiplication des polynômes homogènes à deux variables.

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