Homological units

Abstract

We define and study the invariance properties of homological units. Some applications are given to the derived invariance of Hodge numbers. In particular, we prove that if X and Y are derived equivalent smooth projective varieties of dimension 4 having the same Picard number, then they have the same Hodge numbers. We also give a geometric interpretation of the conjectural invariance of homological units in terms of derived Jacobians.

arXiv comment13 pages. Comments welcome. 2nd version : I prove isogeny of the derived Jacobians of two smooth projective derived equivalent varieties if they have dimension less or equal to 4