Degenerations of Prym varieties and intersections of three quadrics.
Derived invariance of the number of holomorphic -forms and vector fields
We prove that smooth projective varieties with equivalent derived categories have isogenous Picard varieties. In particular their irregularity and number of independent vector fields are the same. This implies that all Hodge numbers are the same for arbitrary derived equivalent threefolds, as well as other consequences of derived equivalence based on numerical criteria.
Distinguishing Prymians from Jacobians.