Perverse sheaves on semi-abelian varieties
Algebraic Geometry
2020-11-26 v3
Abstract
We give a complete (global) characterization of complex perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell's work on perverse sheaves on complex abelian varieties, as well as Gabber-Loeser's results on perverse sheaves on complex affine tori. We apply our results to the study of cohomology jump loci of smooth quasi-projective varieties, to the topology of the Albanese map, and in the context of homological duality properties of complex algebraic varieties.
Cite
@article{arxiv.1804.05014,
title = {Perverse sheaves on semi-abelian varieties},
author = {Yongqiang Liu and Laurentiu Maxim and Botong Wang},
journal= {arXiv preprint arXiv:1804.05014},
year = {2020}
}
Comments
34 pages; comments are very welcome; v2: shortened several proofs, updated references, fixed typos