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On the invariance of Hodge numbers under derived equivalence

SEMINARS: HARVARD-MIT ALGEBRAIC GEOMETRY

When: January 31, 2023
3:00 pm - 4:00 pm
Where: Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Luigi Lombardi - University of Milan

A conjecture of Orlov predicts the invariance of the Hodge numbers of a smooth projective complex variety under derived equivalence. For instance this has been verified in the case of varieties of general type. In this talk, I will examine the case of varieties that are fibered by varieties of general type through the Albanese map. For this class of varieties I will prove the derived invariance of Hodge numbers of type $h^{0,p}$, together with a few other invariants arising from the Albanese map. This talk is based on a joint work with F. Caucci and G. Pareschi.