Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans torsion  [ Harder-Narasimhan filtration for complex bundles or torsion free sheaves ]
Annales de l'Institut Fourier, Volume 53 (2003) no. 2, p. 541-564

We generalize here the Harder-Narasimhan filtration, on the one hand to the case of complex vector bundles over almost complex manifolds and on the other hand to torsion free sheaves. We also prove the openness of stability in deformation in this very general context.

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.

DOI : https://doi.org/10.5802/aif.1952
Classification:  53C07,  32Q60,  32L10
Keywords: Harder-Narasimhan filtration, stability, almost complex structure, sheaves, deformation
@article{AIF_2003__53_2_541_0,
     author = {Bruasse, Laurent},
     title = {Filtration de Harder-Narasimhan pour des fibr\'es complexes ou des faisceaux sans torsion},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {2},
     year = {2003},
     pages = {541-564},
     doi = {10.5802/aif.1952},
     zbl = {01940704},
     mrnumber = {1990006},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2003__53_2_541_0}
}
Bruasse, Laurent. Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans torsion. Annales de l'Institut Fourier, Volume 53 (2003) no. 2, pp. 541-564. doi : 10.5802/aif.1952. http://www.numdam.org/item/AIF_2003__53_2_541_0/

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