Derived invariants arising from the Albanese map

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-07-25 DOI:10.14231/ag-2019-031

Federico Caucci, G. Pareschi

引用次数: 4

Abstract

Let $a_X:X\rightarrow \mathrm{Alb}\, X$ 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. 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.

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Albanese映射中的导出不变量

设$a_X:X\rightarrow\mathrm{Alb}\，X$是光滑复射影变种的Albanese映射。粗略地说，在这个注中，我们证明了对于所有$i\geq0$和$\alpha\in\mathrm｛Pic｝^0\，X$，上同调秩$h^i（\mathrm{Alb｝\，X，\，{a_X}_*\omega_X\otimes P_\alpha）$是派生不变量。在最大Albanese维数的变体的情况下，这证明了Popa和Lombardi Popa的猜想——包括Hodge数$h^{0，j}$的导出不变性——以及它们对任意变体的较弱版本。最后，我们提供了一个应用于某些不规则fibration的导出不变性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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