Real projective structures on Riemann surfaces and new hyper-K\"ahler manifolds

DOI10.1007/S00229-022-01377-ZarXiv1906.10350WikidataQ114230744 ScholiaQ114230744MaRDI QIDQ6321008

Sebastian Heller

Publication date: 25 June 2019

Abstract: 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 $lambda$-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-K"ahler manifolds associated to any compact Riemann surface of genus $ggeq2$. These hyper-K"ahler manifolds can be considered as moduli spaces of (certain) singular solutions of the self-duality equations.

Mathematics Subject Classification ID

Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Twistor methods in differential geometry (53C28) Vector bundles on curves and their moduli (14H60)

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