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.
Keywords: Analytic halo, character variety, fission
Mot 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 = {https://www.numdam.org/articles/10.5802/aif.2503/} }
TY - JOUR AU - Boalch, Philip TI - Through the analytic halo: Fission via irregular singularities JO - Annales de l'Institut Fourier PY - 2009 SP - 2669 EP - 2684 VL - 59 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://www.numdam.org/articles/10.5802/aif.2503/ DO - 10.5802/aif.2503 LA - en ID - AIF_2009__59_7_2669_0 ER -
%0 Journal Article %A Boalch, Philip %T Through the analytic halo: Fission via irregular singularities %J Annales de l'Institut Fourier %D 2009 %P 2669-2684 %V 59 %N 7 %I Association des Annales de l’institut Fourier %U https://www.numdam.org/articles/10.5802/aif.2503/ %R 10.5802/aif.2503 %G en %F AIF_2009__59_7_2669_0
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. https://www.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 | Zbl
[3] Wild non-abelian Hodge theory on curves, Compos. Math., Volume 140 (2004) no. 1, pp. 179-204 | DOI | MR | Zbl
[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 | DOI | MR | Zbl
[6] Symplectic manifolds and isomonodromic deformations, Adv. Math., Volume 163 (2001) no. 2, pp. 137-205 | DOI | MR | Zbl
[7]
[8] Quasi-Hamiltonian geometry of meromorphic connections, Duke Math. J., Volume 139 (2007) no. 2, pp. 369-405 (math.DG/0203161) | DOI | MR | Zbl
[9] Singularités irrégulières, Documents Mathématiques (Paris), 5, Société Mathématique de France, Paris, 2007 (Correspondance et documents) | MR | Zbl
[10] 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] Elementary acceleration and multisummability I, Ann. Inst. H. Poincaré Phys. Théor., Volume 54 (1991) no. 4, pp. 331-401 | Numdam | MR | Zbl
[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 | Zbl
[13] Harmonic bundles on noncompact curves, J. Amer. Math. Soc., Volume 3 (1990) no. 3, pp. 713-770 | DOI | MR | Zbl
[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 | Zbl
- Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity, Advances in Mathematics, Volume 462 (2025), p. 110101 | DOI:10.1016/j.aim.2024.110101
- Epilogue: Stokes Phenomena. Dynamics, Classification Problems and Avatars, Handbook of Geometry and Topology of Singularities VI: Foliations (2024), p. 383 | DOI:10.1007/978-3-031-54172-8_10
- Sp(1)-symmetric hyperkähler quantisation, Pacific Journal of Mathematics, Volume 329 (2024) no. 1, p. 1 | DOI:10.2140/pjm.2024.329.1
- Topology of Irregular Isomonodromy Times on a Fixed Pointed Curve, Transformation Groups (2023) | DOI:10.1007/s00031-023-09800-9
- Euler continuants in noncommutative quasi-Poisson geometry, Forum of Mathematics, Sigma, Volume 10 (2022) | DOI:10.1017/fms.2022.76
- Topology of the Stokes phenomenon, Integrability, Quantization, and Geometry, Volume 103.1 (2021), p. 55 | DOI:10.1090/pspum/103.1/01832
- Stokes phenomenon, Gelfand–Zeitlin systems and relative Ginzburg–Weinstein linearization, Advances in Mathematics, Volume 338 (2018), p. 237 | DOI:10.1016/j.aim.2018.09.012
- Argyres-Douglas theories, chiral algebras and wild Hitchin characters, Journal of High Energy Physics, Volume 2018 (2018) no. 1 | DOI:10.1007/jhep01(2018)150
- Global Weyl groups and a new theory of multiplicative quiver varieties, Geometry Topology, Volume 19 (2016) no. 6, p. 3467 | DOI:10.2140/gt.2015.19.3467
- Symplectic and Poisson Geometry of the Moduli Spaces of Flat Connections Over Quilted Surfaces, Mathematical Aspects of Quantum Field Theories (2015), p. 343 | DOI:10.1007/978-3-319-09949-1_11
- Geometry and braiding of Stokes data; Fission and wild character varieties, Annals of Mathematics, Volume 179 (2014) no. 1, p. 301 | DOI:10.4007/annals.2014.179.1.5
- Poisson varieties from Riemann surfaces, Indagationes Mathematicae, Volume 25 (2014) no. 5, p. 872 | DOI:10.1016/j.indag.2014.07.004
- Riemann–Hilbert for tame complex parahoric connections, Transformation Groups, Volume 16 (2011) no. 1, p. 27 | DOI:10.1007/s00031-011-9121-1
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