Real projective structures on Riemann surfaces and new hyper-Kahler manifolds

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