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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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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DOI: https://doi.org/10.1007/s00220-019-03340-8