We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing -parameter subgroups are the same thing when considered in the gauge theoretical framework.
Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears...
On généralise dans cet article la notion de filtration de Harder-Narasimhan au cas des
fibrés complexes sur une variété presque complexe compacte d'une part, et au cas des
faisceaux cohérents sans torsion sur une variété holomorphe d'autre part. On démontre,
dans les deux cas, l'existence d'un déstabilisant maximal. On obtient un théorème de
convergence en famille et par là-même l'ouverture de la stabilité en déformation.
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....
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