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Solutions to Donaldson’s Hyperkähler Reduction on a Curve

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Abstract

We study an infinite-dimensional hyperkähler reduction introduced by Donaldson and associated with the constant scalar curvature equation on a Riemann surface. It is known that the corresponding moment map equations admit special solutions constructed from holomorphic quadratic differentials. Here we obtain a more general existence result and so a larger hyperkähler moduli space.

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Acknowledgements

We are grateful to Olivier Biquard for a discussion related to the present paper, and to the referee for valuable suggestions and remarks.

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Authors and Affiliations

  1. SISSA, via Bonomea 265, 34136, Trieste, Italy

    Carlo Scarpa & Jacopo Stoppa

  2. IGAP, via Beirut 2, 34151, Trieste, Italy

    Carlo Scarpa & Jacopo Stoppa

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  1. Carlo Scarpa
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  2. Jacopo Stoppa
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Correspondence to Jacopo Stoppa.

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Scarpa, C., Stoppa, J. Solutions to Donaldson’s Hyperkähler Reduction on a Curve. J Geom Anal 31, 2871–2889 (2021). https://doi.org/10.1007/s12220-020-00377-3

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  • DOI: https://doi.org/10.1007/s12220-020-00377-3

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