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Originalpublikation
Heller, S.: Real projective structures on Riemann surfaces and new hyper-Kähler manifolds. In: Manuscripta mathematica 171 (2023), Nr. 1-2, S. 241-262. DOI: https://doi.org/10.1007/s00229-022-01377-z
The twistor space of the moduli space of solutions of Hitchin’s self-duality equations can be identified with the Deligne-Hitchin moduli space of λ-connections. We use real projective structures on Riemann surfaces to prove the existence of new components of real holomorphic sections of the Deligne-Hitchin moduli space. Applying the twistorial construction we show the existence of new hyper-Kähler manifolds associated to any compact Riemann surface of genus g≥ 2. These hyper-Kähler manifolds can be considered as moduli spaces of (certain) singular solutions of the self-duality equations.