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Cohomological rank functions on abelian varieties

Zhi Jiang Fudan University & SCMS Giuseppe Pareschi Università di Roma “Tor Vergata”

Algebraic Geometry mathscidoc:2105.45002

Annales Scientifiques de l'École Normale Supérieure, 53, (4), 815–846, 2020.10
Generalizing the continuous rank function of Barja-Pardini-Stoppino, in this paper we consider cohomological rank functions of Q-twisted (complexes of) coherent sheaves on abelian varieties. They satisfy a natural transformation formula with respect to the Fourier-Mukai-Poincar´e 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 GVsubschemes and the second one to multiplication maps of global sections of ample line bundles on abelian varieties.
abelian varieties, Fourier-Mukai transforms
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@inproceedings{zhi2020cohomological,
  title={Cohomological rank functions on abelian varieties},
  author={Zhi Jiang, and Giuseppe Pareschi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210521180928287537825},
  booktitle={Annales Scientifiques de l'École Normale Supérieure},
  volume={53},
  number={4},
  pages={815–846},
  year={2020},
}
Zhi Jiang, and Giuseppe Pareschi. Cohomological rank functions on abelian varieties. 2020. Vol. 53. In Annales Scientifiques de l'École Normale Supérieure. pp.815–846. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210521180928287537825.
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