Caucci, Federico; Pareschi, Giuseppe Derived invariants arising from the Albanese map. (English) Zbl 1441.14060 Algebr. Geom. 6, No. 6, 730-746 (2019). Summary: Let \(a_X: X\to \to \operatorname{Alb} X\) be the Albanese map of a smooth complex projective variety. Roughly speaking, in this note we prove that for all \(i\geqslant 0\) and \(\alpha\in\operatorname{Pic}^0 X\), the cohomology ranks \(h^i(\operatorname{Alb} X, a_{X_\ast}\omega_X\otimes P_\alpha)\) are derived invariants. This proves conjectures of M. Popa [Clay Math. Proc. 18, 567–575 (2013; Zbl 1317.14038)] and L. Lombardi and M. Popa [Lond. Math. Soc. Lect. Note Ser. 417, 291–306 (2014; Zbl 1326.14013)] – 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 the derived invariance of certain irregular fibrations. Cited in 2 Documents MSC: 14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry 14D06 Fibrations, degenerations in algebraic geometry 14E05 Rational and birational maps 14F17 Vanishing theorems in algebraic geometry Keywords:derived categories; cohomological support loci; Hodge numbers; fibrations Citations:Zbl 1317.14038; Zbl 1326.14013 PDFBibTeX XMLCite \textit{F. Caucci} and \textit{G. Pareschi}, Algebr. Geom. 6, No. 6, 730--746 (2019; Zbl 1441.14060) Full Text: DOI arXiv