Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 1017-1053.

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.

Nous généralisons ici la théorie des sous-groupes déstabilisants optimaux à un paramètre dans un cadre non algébrique : celui des actions holomorphes de groupes de Lie complexes réductifs sur une variété kählerienne de dimension finie (compacte ou non). Dans une seconde partie, nous montrons comment ces résultats peuvent s’étendre dans le cadre de la théorie de jauge, nous explorons la relation entre filtration de Harder-Narasimhan et vecteur déstabilisant optimal d’un objet non semistable.

DOI: 10.5802/aif.2120
Classification: 32M05,  53D20,  14L24,  14L30,  32L05,  32Q15
Keywords: symplectic actions, Hamiltonian actions, stability, Harder Narasimhan filtration, Shatz stratification, gauge theory.
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Bruasse, Laurent; Teleman, Andrei. Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry. Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 1017-1053. doi : 10.5802/aif.2120. https://aif.centre-mersenne.org/articles/10.5802/aif.2120/

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