Connected sums of self-dual manifolds and deformations of singular spaces

We give general conditions under which the connected sum of two self-dual Riemannian 4-manifolds again admits a self-dual structure. Our techniques combine twistor methods with the deformation theory of compact complex spaces. They are related on the one hand to the analytical approach which has been used recently by Floer, and on the other hand to the algebro-geometric results of Hitchin and Poon. We give specific examples involving the projective plane and K3 surfaces.