Derived invariants of irregular varieties

Francesco Caucci
(Sapienza Universita' di Roma)

Abstract: It is a natural and interesting problem to figure out how much of the geometry of a smooth complex projective variety is determined by its bounded derived category. We give a general result in this direction: the derived invariance of the cohomology ranks of the pushforward under the Albanese map of the canonical line bundle.

In the case of varieties of maximal Albanese dimension, this settles a conjecture of Lombardi-Popa and proves the derived invariance of the Hodge numbers h^{0, j}, for all j. This is a joint work with G. Pareschi.