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Harder-Narasimhan filtration for complex bundles or torsion free sheaves. (Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans torsion.) (French) Zbl 1114.32010

Summary: 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.

MSC:

32L05 Holomorphic bundles and generalizations
32G13 Complex-analytic moduli problems
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References:

[1] Stable sheaves and Einstein-Hermitian metrics, Geometry and analysis on complex manifolds, (1994) · Zbl 0880.32004
[2] Harder-Narasimhan filtration on non Kähler manifolds, Int. Journal of Maths, 12, 5, 579-594, (2001) · Zbl 1111.32303
[3] Stabilité et filtratrion de Harder-Narasimhan, (2001)
[4] Stability of complex vector bundles, J. Differential Geometry, 43, 2, 231-274, (1996) · Zbl 0853.32033
[5] Sur la 1-forme de torsion d’une variété hermitienne compacte, Math. Ann., vol. 267, 495-518, (1984) · Zbl 0523.53059
[6] On the cohomology groups of moduli spaces, Math. Ann, 212, 215-248, (1975) · Zbl 0324.14006
[7] Differential geometry of complex vector bundles, (1987), Princeton University Press · Zbl 0708.53002
[8] The Kobayashi-Hitchin correspondence, (1995), World Scientific · Zbl 0849.32020
[9] The theorem of grauert-Mülich-spindler, Math. Ann, 225, 317-333, (1981) · Zbl 0438.14015
[10] The decomposition and specialization of algebraic families of vector bundles, Composito. Math, 35, 163-187, (1977) · Zbl 0371.14010
[11] On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Communications on Pure and Applied Mathematics, 39, 257-293, (1986) · Zbl 0615.58045
[12] A note on our previous paper : on the existence of Hermitian-Yang-Mills connections in stable vector bundles, Communications on Pure and Applied Mathematics, 42, 703-707, (1989) · Zbl 0678.58041
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