[De l’autre côté du halo analytique : fission via les singularités irrégulières]
Cet article s’intéresse aux espaces de modules de connexions sur des fibrés sur les surfaces de Riemann, où le groupe de structure du fibré peut varier dans les différentes régions de la surface. Ici, nous allons décrire de tels espaces de modules comme variétés symplectiques complexes, en généralisant les variétés de caractères complexes des surfaces de Riemann.
This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic manifolds, generalising the complex character varieties of Riemann surfaces.
Classification : 53D30, 34M40
Mots clés : halo analytique, variété de caractère, fission
@article{AIF_2009__59_7_2669_0,
author = {Boalch, Philip},
title = {Through the analytic halo: Fission via irregular singularities},
journal = {Annales de l'Institut Fourier},
pages = {2669--2684},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {59},
number = {7},
year = {2009},
doi = {10.5802/aif.2503},
mrnumber = {2649336},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.2503/}
}
Boalch, Philip. Through the analytic halo: Fission via irregular singularities. Annales de l'Institut Fourier, Tome 59 (2009) no. 7, pp. 2669-2684. doi : 10.5802/aif.2503. http://archive.numdam.org/articles/10.5802/aif.2503/
[1] Pure spinors on Lie groups (arXiv:0709.1452)
[2] Lie group valued moment maps, J. Differential Geom., Volume 48 (1998) no. 3, pp. 445-495 | MR 1638045 | Zbl 0948.53045
[3] Wild non-abelian Hodge theory on curves, Compos. Math., Volume 140 (2004) no. 1, pp. 179-204 | Article | MR 2004129 | Zbl 1051.53019
[4] Irregular connections and Kac-Moody root systems (arXiv:0806.1050)
[5] Stokes matrices, Poisson Lie groups and Frobenius manifolds, Invent. Math., Volume 146 (2001) no. 3, pp. 479-506 | Article | MR 1869848 | Zbl 1044.53060
[6] Symplectic manifolds and isomonodromic deformations, Adv. Math., Volume 163 (2001) no. 2, pp. 137-205 | Article | MR 1864833 | Zbl 1001.53059
[7] -bundles, isomonodromy, and quantum Weyl groups, Int. Math. Res. Not. (2002) no. 22, pp. 1129-1166 (math.DG/0108152) | Article | MR 1904670 | Zbl 1003.58028
[8] Quasi-Hamiltonian geometry of meromorphic connections, Duke Math. J., Volume 139 (2007) no. 2, pp. 369-405 (math.DG/0203161) | Article | MR 2352135 | Zbl 1126.53055
[9] Singularités irrégulières, Documents Mathématiques (Paris), 5, Société Mathématique de France, Paris, 2007 (Correspondance et documents) | MR 2387754 | Zbl 1130.14001
[10] The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), Volume 55 (1987) no. 1, pp. 59-126 | Article | MR 887284 | Zbl 0634.53045
[11] Elementary acceleration and multisummability I, Ann. Inst. H. Poincaré Phys. Théor., Volume 54 (1991) no. 4, pp. 331-401 | Numdam | MR 1128863 | Zbl 0748.12005
[12] Hyper-Kähler structures on moduli spaces of parabolic Higgs bundles on Riemann surfaces, Moduli of vector bundles (Sanda, 1994; Kyoto, 1994) (Lecture Notes in Pure and Appl. Math.), Volume 179, Dekker, New York, 1996, pp. 199-208 | MR 1397988 | Zbl 0881.14006
[13] Harmonic bundles on noncompact curves, J. Amer. Math. Soc., Volume 3 (1990) no. 3, pp. 713-770 | Article | MR 1040197 | Zbl 0713.58012
[14] The Hodge filtration on nonabelian cohomology, Algebraic geometry—Santa Cruz 1995 (Proc. Sympos. Pure Math.), Volume 62, Amer. Math. Soc., Providence, RI, 1997, pp. 217-281 | MR 1492538 | Zbl 0914.14003
