On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case

We prove an analog of the Tian-Todorov theorem for twisted generalized Calabi-Yau manifolds; namely, we show that the moduli space of generalized complex structures on a compact twisted generalized Calabi-Yau manifold is unobstructed and smooth. We also construct the extended moduli space and study its Frobenius structure. The physical implications are also discussed.