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Singularities and Poisson geometry of certain representation spaces

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Quantization of Singular Symplectic Quotients

Part of the book series: Progress in Mathematics ((PM,volume 198))

Abstract

Certain representation spaces have been investigated by algebraic geometers as moduli spaces of holomorphic bundles over a Riemann surface. Such moduli spaces exhibit symplectic and Kähler structures as well as gauge theory interpretations. The purpose of this article is to elucidate the local structure of such a space, and the focus will be on the singularities. Among the tools will be the interconnection between the theory of algebraic and symplectic quotients and, furthermore, Poisson structures, a concept which has been known in mathematical physics for long and is currently of much interest in mathematics as well.

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Author information

Authors and Affiliations

  1. UFR de Mathématiques, Université des Sciences et Technologies de Lille, F-59 655, Villeneuve d’Ascq, Cédex, France

    Johannes Huebschmann

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  1. Johannes Huebschmann
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Editor information

Editors and Affiliations

  1. Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    N. P. Landsman

  2. Mathematisch-Naturwissenschaftliche Fakultät II Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    M. Pflaum

  3. Fakultät für Mathematik und Informatik, Universität Mannheim, D7, 27, 68131, Mannheim, Germany

    M. Schlichenmaier

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Huebschmann, J. (2001). Singularities and Poisson geometry of certain representation spaces. In: Landsman, N.P., Pflaum, M., Schlichenmaier, M. (eds) Quantization of Singular Symplectic Quotients. Progress in Mathematics, vol 198. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8364-1_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8364-1_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9535-4

  • Online ISBN: 978-3-0348-8364-1

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