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arXiv · 1707.05888

Cohomological rank functions on abelian varieties

Zhi Jiang·Giuseppe Pareschi
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Abstract

Generalizing the continuous rank function of Barja-Pardini-Stoppino, in this paper we consider cohomological rank functions of $\mathbb Q$-twisted (complexes of) coherent sheaves on abelian varieties. They satisfy a natural transformation formula with respect to the Fourier-Mukai-Poincaré transform, which has several consequences. In many concrete geometric contexts these functions provide useful invariants. We illustrate this with two different applications, the first one to GV-subschemes and the second one to multiplication maps of global sections of ample line bundles on abelian varieties.

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BibTeXRIS

Zhi Jiang, Giuseppe Pareschi. 2018-12-16. Cohomological rank functions on abelian varieties. https://arxiv.org/abs/1707.05888

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