[Filtration de Harder-Narasimhan et vecteurs déstabilisants optimaux en géométrie complexe]
Nous généralisons ici la théorie des sous-groupes déstabilisants optimaux à un paramètre dans un cadre non algébrique : celui des actions holomorphes de groupes de Lie complexes réductifs sur une variété kählerienne de dimension finie (compacte ou non). Dans une seconde partie, nous montrons comment ces résultats peuvent s'étendre dans le cadre de la théorie de jauge, nous explorons la relation entre filtration de Harder-Narasimhan et vecteur déstabilisant optimal d'un objet non semistable.
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.
Keywords: symplectic actions, Hamiltonian actions, stability, Harder Narasimhan filtration, Shatz stratification, gauge theory.
Mot clés : action symplectique, action hamiltonienne, stabilité, filtration de Harder-Narasimhan, stratification de Shatz, théorie de jauge
@article{AIF_2005__55_3_1017_0,
author = {Bruasse, Laurent and Teleman, Andrei},
title = {Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry},
journal = {Annales de l'Institut Fourier},
pages = {1017--1053},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {55},
number = {3},
year = {2005},
doi = {10.5802/aif.2120},
mrnumber = {2149409},
zbl = {1093.32009},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2120/}
}
TY - JOUR AU - Bruasse, Laurent AU - Teleman, Andrei TI - Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry JO - Annales de l'Institut Fourier PY - 2005 SP - 1017 EP - 1053 VL - 55 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2120/ DO - 10.5802/aif.2120 LA - en ID - AIF_2005__55_3_1017_0 ER -
%0 Journal Article %A Bruasse, Laurent %A Teleman, Andrei %T Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry %J Annales de l'Institut Fourier %D 2005 %P 1017-1053 %V 55 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2120/ %R 10.5802/aif.2120 %G en %F AIF_2005__55_3_1017_0
Bruasse, Laurent; Teleman, Andrei. Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry. Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 1017-1053. doi : 10.5802/aif.2120. http://www.numdam.org/articles/10.5802/aif.2120/
[1] Special metrics and stability for holomorphic bundles with global sections, J. Diff. Geom., Volume 33 (1991), pp. 169-213 | MR | Zbl
[2] Harder-Narasimhan filtration on non Kähler manifolds, Int. Journal of Maths, Volume 12 (2001) no. 5, pp. 579-594 | DOI | MR | Zbl
[3] Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans-torsion, Ann. Inst. Fourier, Volume 53 (2003) no. 2, pp. 539-562 | Numdam | MR | Zbl
[4] Optimal destabilizing vectors in some gauge theoretical moduli problems (2004) (IML, ref arxiv math.DG/0403264, http://arxiv.org/abs/math.DG/0403264)
[5] Harder-Narasimhan filtrations and optimal destabilizing vectors in gauge theory (2003) (article in preparation)
[6] On the cohomology groups of moduli spaces, Math. Ann., Volume 212 (1975), pp. 215-248 | DOI | MR | Zbl
[7] Geometric invariant theory on Stein spaces, Math. Ann., Volume 289 (1991), pp. 631-662 | DOI | MR | Zbl
[8] Analytic Hilbert Quotient (Several complex variables), Volume 37 (1999), pp. 309-349 | Zbl
[9] Reduction of complex Hamiltonian G-spaces, Geometric and Functional Analysis, Volume 4 (1994) no. 3, pp. 288-297 | DOI | MR | Zbl
[10] Hyperkähler metrics and supersymmetry, Commun. Math. Phys., Volume 108 (1987), pp. 535-589 | DOI | MR | Zbl
[11] Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, Volume 31 (1984) no. Princeton University Press | MR | Zbl
[12] The universal Kobayashi-Hitchin correspondance (2003) (article in preparation)
[13] The theorem of Grauert-Mülich-Spindler, Math. Ann., Volume 255 (1981), pp. 317-333 | DOI | MR | Zbl
[14] Geometric invariant theory, Springer-Verlag, 1982 | MR | Zbl
[15] A Hitchin-Kobayashi correspondence for Kähler fibrations, J. reine angew. Maths, Volume 528 (2000), pp. 41-80 | MR | Zbl
[16] Master spaces for stable pairs, Topology, Volume 38 (1999) no. 1, pp. 117-139 | DOI | MR | Zbl
[17] Gauge theoretical equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces, Comm. Math. Phys., Volume 227 (2002) no. 3, pp. 551-585 | DOI | MR | Zbl
[18] Seifert Manifold, Lectures Notes in Maths, 291, Springer Verlag, 1972 | MR | Zbl
[19] Some remarks on the instability flag, Tôhoku Math. Journ., Volume 36 (1984), pp. 269-291 | DOI | MR | Zbl
[20] The decomposition and specialization of algebraic families of vector bundles, Composito. Math., Volume 35 (1977), pp. 163-187 | Numdam | MR | Zbl
[21] Die Theorie der optimalen einparameteruntergruppen für instabile vektoren, Algebraische Transformationsgruppen und Invariantentheorie (DMV Seminar, 13 DMV Seminar), Volume 13 (1989), pp. 115-131 | Zbl
[22] Analytic stability, symplectic stability in non-algebraic complex geometry (2003) (preprint, math.CV/0309230, http://arxiv.org/abs/math.CV/0309230)
Cité par Sources :
