Through the analytic halo: Fission via irregular singularities
[De l’autre côté du halo analytique  : fission via les singularités irrégulières]
Boalch, Philip
Annales de l'Institut Fourier, Tome 59 (2009), p. 2669-2684 / Harvested from Numdam

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.

Publié le : 2009-01-01
DOI : https://doi.org/10.5802/aif.2503
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},
     volume = {59},
     year = {2009},
     pages = {2669-2684},
     doi = {10.5802/aif.2503},
     zbl = {pre05689402},
     mrnumber = {2649336},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2009__59_7_2669_0}
}
Boalch, Philip. Through the analytic halo: Fission via irregular singularities. Annales de l'Institut Fourier, Tome 59 (2009) pp. 2669-2684. doi : 10.5802/aif.2503. http://gdmltest.u-ga.fr/item/AIF_2009__59_7_2669_0/

[1] Alekseev, Anton; Burstzyn, H.; Meinrenken, Eckhard Pure spinors on Lie groups (arXiv:0709.1452)

[2] Alekseev, Anton; Malkin, Anton; Meinrenken, Eckhard Lie group valued moment maps, J. Differential Geom., Tome 48 (1998) no. 3, pp. 445-495 | MR 1638045 | Zbl 0948.53045

[3] Biquard, Olivier; Boalch, P. P. Wild non-abelian Hodge theory on curves, Compos. Math., Tome 140 (2004) no. 1, pp. 179-204 | Article | MR 2004129 | Zbl 1051.53019

[4] Boalch, P. P. Irregular connections and Kac-Moody root systems (arXiv:0806.1050)

[5] Boalch, P. P. Stokes matrices, Poisson Lie groups and Frobenius manifolds, Invent. Math., Tome 146 (2001) no. 3, pp. 479-506 | Article | MR 1869848 | Zbl 1044.53060

[6] Boalch, P. P. Symplectic manifolds and isomonodromic deformations, Adv. Math., Tome 163 (2001) no. 2, pp. 137-205 | Article | MR 1864833 | Zbl 1001.53059

[7] Boalch, P. P. G-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] Boalch, P. P. Quasi-Hamiltonian geometry of meromorphic connections, Duke Math. J., Tome 139 (2007) no. 2, pp. 369-405 (math.DG/0203161) | Article | MR 2352135 | Zbl 1126.53055

[9] Deligne, Pierre; Malgrange, Bernard; Ramis, Jean-Pierre Singularités irrégulières, Société Mathématique de France, Paris, Documents Mathématiques (Paris), 5 (2007) (Correspondance et documents) | MR 2387754 | Zbl 1130.14001

[10] Hitchin, N. J. The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), Tome 55 (1987) no. 1, pp. 59-126 | Article | MR 887284 | Zbl 0634.53045

[11] Martinet, Jean; Ramis, Jean-Pierre Elementary acceleration and multisummability I, Ann. Inst. H. Poincaré Phys. Théor., Tome 54 (1991) no. 4, pp. 331-401 | Numdam | MR 1128863 | Zbl 0748.12005

[12] Nakajima, Hiraku Hyper-Kähler structures on moduli spaces of parabolic Higgs bundles on Riemann surfaces, Moduli of vector bundles (Sanda, 1994; Kyoto, 1994), Dekker, New York (Lecture Notes in Pure and Appl. Math.) Tome 179 (1996), pp. 199-208 | MR 1397988 | Zbl 0881.14006

[13] Simpson, Carlos T. Harmonic bundles on noncompact curves, J. Amer. Math. Soc., Tome 3 (1990) no. 3, pp. 713-770 | Article | MR 1040197 | Zbl 0713.58012

[14] Simpson, Carlos T. The Hodge filtration on nonabelian cohomology, Algebraic geometry—Santa Cruz 1995, Amer. Math. Soc., Providence, RI (Proc. Sympos. Pure Math.) Tome 62 (1997), pp. 217-281 | MR 1492538 | Zbl 0914.14003