Displaying similar documents to “Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry”

Optimal destabilizing vectors in some Gauge theoretical moduli problems

Laurent Bruasse (2006)

Annales de l’institut Fourier

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We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing 1 -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...

Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups

Jean-Marc Drézet, Günther Trautmann (2003)

Annales de l’institut Fourier

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We extend the methods of geometric invariant theory to actions of non–reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non–reductive. Given a linearization of the natural action of the group Aut ( E ) × Aut ( F ) on Hom(E,F), a homomorphism is called stable if its orbit with respect to the unipotent radical is contained in the stable locus with respect to the natural reductive subgroup of the automorphism group. We encounter effective numerical conditions...

Semistable quotients

Peter Heinzner, Luca Migliorini, Marzia Polito (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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