no. 7
Through the analytic halo: Fission via irregular singularities
[De l’autre côté du halo analytique  : fission via les singularités irrégulières]
Boalch, Philip1
1 École Normale Supérieure et CNRS 45 rue d’Ulm 75005 Paris (France)
Annales de l'Institut Fourier, Tome 59 (2009) no. 7, pp. 2669-2684.

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.

DOI : 10.5802/aif.2503
Classification : 53D30, 34M40
Keywords: Analytic halo, character variety, fission
Mot clés : halo analytique, variété de caractère, fission
Boalch, Philip 1

1 École Normale Supérieure et CNRS 45 rue d’Ulm 75005 Paris (France) 
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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] 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., Volume 48 (1998) no. 3, pp. 445-495 | MR | Zbl

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

[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., Volume 146 (2001) no. 3, pp. 479-506 | DOI | MR | Zbl

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

[7] Boalch, P. P. G-bundles, isomonodromy, and quantum Weyl groups, Int. Math. Res. Not. (2002) no. 22, pp. 1129-1166 (math.DG/0108152) | DOI | MR | Zbl

[8] Boalch, P. P. Quasi-Hamiltonian geometry of meromorphic connections, Duke Math. J., Volume 139 (2007) no. 2, pp. 369-405 (math.DG/0203161) | DOI | MR | Zbl

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

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

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

[12] Nakajima, Hiraku 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 | Zbl

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

[14] Simpson, Carlos T. 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 | Zbl

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