Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
[Filtration de Harder-Narasimhan et vecteurs déstabilisants optimaux en géométrie complexe]
Bruasse, Laurent ; Teleman, Andrei
Annales de l'Institut Fourier, Tome 55 (2005), p. 1017-1053 / Harvested from Numdam
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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.

Publié le : 2005-01-01
DOI : https://doi.org/10.5802/aif.2120
Classification:  32M05,  53D20,  14L24,  14L30,  32L05,  32Q15
Mots clés: action symplectique, action hamiltonienne, stabilité, filtration de Harder-Narasimhan, stratification de Shatz, théorie de jauge 
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     author = {Bruasse, Laurent and Teleman, Andrei},
     title = {Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry},
     journal = {Annales de l'Institut Fourier},
     volume = {55},
     year = {2005},
     pages = {1017-1053},
     doi = {10.5802/aif.2120},
     mrnumber = {2149409},
     zbl = {1093.32009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2005__55_3_1017_0}
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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) pp. 1017-1053. doi : 10.5802/aif.2120. http://gdmltest.u-ga.fr/item/AIF_2005__55_3_1017_0/

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