Optimal destabilizing vectors in some gauge theoretical moduli problems

Simple item page
dc.creatorBruasse, Laurent
dc.date2004-03-16
dc.date2004-09-13
dc.date.accessioned2026-07-07T05:06:27Z
dc.date.available2026-07-07T05:06:27Z
dc.descriptionWe show that the ``classical'' Harder-Narasimhan filtration associated to a non semistable vector bundle $E$ 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 as an extremal value of the so called "maximal weight function". We give a complete description of these optimal destabilizing endomorphisms. Then we show that this principle holds for another important moduli problem: holomorphic pairs (i.e. holomorphic vector bundles coupled with morphisms with fixed source). We get a generalization of the Harder-Narasimhan filtration theorem for the associated notion of $τ$-stability. These results suggest that the principle holds in the whole gauge theoretical framework.
dc.description18 pages, 6 figures; new introduction, new references added, minor modifications
dc.identifierhttps://arxiv.org/abs/math/0403264
dc.identifierhttp://arxiv.org/abs/math/0403264
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70476
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.subjectComplex Variables
dc.subjectSymplectic Geometry
dc.subject53C07, 32G13, 58D27, 53C55, 53D20, 32L05, 32M05
dc.titleOptimal destabilizing vectors in some gauge theoretical moduli problems
dc.typetext

Files

Collections

arXiv