Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry

Laurent Bruasse[1]; Andrei Teleman

  • [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 (2005)

  • Volume: 55, Issue: 3, page 1017-1053
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Bruasse, Laurent, and Teleman, Andrei. "Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry." Annales de l’institut Fourier 55.3 (2005): 1017-1053. <http://eudml.org/doc/116203>.

@article{Bruasse2005,
abstract = {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.},
affiliation = {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)},
author = {Bruasse, Laurent, Teleman, Andrei},
journal = {Annales de l’institut Fourier},
keywords = {symplectic actions; Hamiltonian actions; stability; Harder Narasimhan filtration; Shatz stratification; gauge theory; moduli problems},
language = {eng},
number = {3},
pages = {1017-1053},
publisher = {Association des Annales de l'Institut Fourier},
title = {Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry},
url = {http://eudml.org/doc/116203},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Bruasse, Laurent
AU - Teleman, Andrei
TI - Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 3
SP - 1017
EP - 1053
AB - 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.
LA - eng
KW - symplectic actions; Hamiltonian actions; stability; Harder Narasimhan filtration; Shatz stratification; gauge theory; moduli problems
UR - http://eudml.org/doc/116203
ER -

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