Generalized Complex Structures on Kodaira Surfaces

Abstract

In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized complex structures on a Kodaira surface is smooth of complex dimension four. Furthermore, we give an explicit description of this moduli space using deformation theory. We also obtain a Global Torelli Theorem for Kodaira surfaces in the generalized setting, which is an analogue of Huybrechts' result for generalized K3 surfaces. Finally, we study generalized holomorphic bundles with respect to the even-type generalized complex structures previously obtained.