Derived invariants arising from the Albanese map

Abstract

Let $a_X:X\to \mathrm{Alb}X$ be the Albanese map of a smooth complex projective variety. Roughly speaking in this note we prove that for all $i\ge 0$ and $\alpha \in {\mathrm{Pic}}^{0}X$, the cohomology ranks $h^i(\mathrm{Alb}X,{a_X}_{\ast }{\omega }_X\otimes P_{\alpha })$ are derived invariants. In the case of varieties of maximal Albanese dimension this proves conjectures of Popa and Lombardi-Popa -including the derived invariance of the Hodge numbers $h^{0,j}$ -- and a weaker version of them for arbitrary varieties. Finally we provide an application to derived invariance of certain irregular fibrations.

arXiv comment16 pages. Final version to appear on Algebraic Geometry

References in corpus (2)

• The Mukai pairing, I: the Hochschild structure
• Derived invariants of irregular varieties and Hochschild homology

Cited by in corpus (1)

• Derived invariance of the numbers $h^{0,p}(X)$