no. 3
Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
[Filtration de Harder-Narasimhan et vecteurs déstabilisants optimaux en géométrie complexe]
Bruasse, Laurent1 ; Teleman, Andrei
1 IML, CNRS UPR 9016, 163 avenue de Luminy, 13288 Marseille cedex 09 (France), CMI, LATP UMR 6632, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13 (France)
Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 1017-1053.

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.

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.

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.
Mot clés : action symplectique, action hamiltonienne, stabilité, filtration de Harder-Narasimhan, stratification de Shatz, théorie de jauge

Bruasse, Laurent 1 ; Teleman, Andrei 

1 IML, CNRS UPR 9016, 163 avenue de Luminy, 13288 Marseille cedex 09 (France), CMI, LATP UMR 6632, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13 (France) 
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Bruasse, Laurent; Teleman, Andrei. Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry. Annales de l'Institut Fourier, Tome 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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