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

Derived invariants arising from the Albanese map / Caucci, Federico; Giuseppe, Pareschi. - In: ALGEBRAIC GEOMETRY. - ISSN 2214-2584. - 6:6(2019), pp. 730-746. [10.14231/AG-2019-031]

Derived invariants arising from the Albanese map

CAUCCI, FEDERICO;
2019

Abstract

Let $a_X : X ightarrow mathrm{Alb} X$ be the Albanese map of a smooth complex projective variety. Roughly speaking, in this note we prove that for all $i geq 0$ and $alpha in mathrm{Pic}^0 X$, the cohomology ranks $h^i(mathrm{Alb} X, {a_X}_* omega_X otimes P_alpha)$ are derived invariants. This proves conjectures of Popa and Lombardi-Popa -- including the derived invariance of the Hodge numbers $h^{0,j}$ -- in the case of varieties of maximal Albanese dimension and a weaker version of them for arbitrary varieties. Finally, we provide an application to derived invariance of certain irregular fibrations.
2019
derived categories; cohomological support loci; Hodge numbers; fibrations
01 Pubblicazione su rivista::01a Articolo in rivista
Derived invariants arising from the Albanese map / Caucci, Federico; Giuseppe, Pareschi. - In: ALGEBRAIC GEOMETRY. - ISSN 2214-2584. - 6:6(2019), pp. 730-746. [10.14231/AG-2019-031]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1318661
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