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Real Holomorphic Sections of the Deligne–Hitchin Twistor Space

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Abstract

We study the holomorphic sections of the Deligne–Hitchin moduli space of a compact Riemann surface, especially the sections that are invariant under the natural anti-holomorphic involutions of the moduli space. Their relationships with the harmonic maps are established. As a by product, a question of Simpson on such sections, posed in [Si4], is answered.

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Acknowledgements

We are very grateful to the two referees for their very helpful comments to improve the manuscript. The first author is supported by a J. C. Bose Fellowship. The second author is supported by RTG 1670 “Mathematics inspired by string theory and quantum field theory” funded by the Deutsche Forschungsgemeinschaft (DFG).

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    Indranil Biswas

  2. Mathematics Department, EISTI-University Paris-Seine, Avenue du parc, 95000, Cergy-Pontoise, France

    Indranil Biswas

  3. Fachbereich Mathematik, Universität Hamburg, 20146, Hamburg, Germany

    Sebastian Heller

  4. Institut für Differentialgeometrie, Welfengarten 1, 30167, Hannover, Germany

    Markus Röser

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  1. Indranil Biswas
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  2. Sebastian Heller
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  3. Markus Röser
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Correspondence to Indranil Biswas.

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Communicated by N. Nekrasov

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Biswas, I., Heller, S. & Röser, M. Real Holomorphic Sections of the Deligne–Hitchin Twistor Space. Commun. Math. Phys. 366, 1099–1133 (2019). https://doi.org/10.1007/s00220-019-03340-8

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