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-Kähler manifolds associated to any compact Riemann surface of genus gge 2. These hyper-Kähler manifolds can be considered as moduli spaces of (certain) singular solutions of the self-duality equations.
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