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Symmetric Differentials and the Dimension of Hitchin Components for Orbi-Curves

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Current Trends in Analysis, its Applications and Computation

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Abstract

This note is based on a talk given at the 2019 ISAAC Congress in Aveiro. We give an expository account of joint work with Daniele Alessandrini and Gye-Seon Lee on Hitchin components for orbifold groups, recasting part of it in the language of analytic orbi-curves. This reduces the computation of the dimension of the Hitchin component for orbifold groups to an application of the orbifold Riemann-Roch theorem.

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Acknowledgements

It is a pleasure to thank Alexander Schmitt and all participants of the Session on Complex Geometry at ISAAC 2019, as well as Georgios Kydonakis, for feedback on the topics discussed in this paper. I also thank the referee for careful reading and valuable suggestions.

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Authors and Affiliations

  1. Universidad de Los Andes, Departamento de Matemáticas, Bogotá, Colombia

    Florent Schaffhauser

  2. Université de Strasbourg, IRMA UMR 7501, Strasbourg, France

    Florent Schaffhauser

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  1. Florent Schaffhauser
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Correspondence to Florent Schaffhauser .

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Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Schaffhauser, F. (2022). Symmetric Differentials and the Dimension of Hitchin Components for Orbi-Curves. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_13

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