2018/04/13 by Yongqiang Liu, Liu, Yongqiang, Laurenţiu Maxim +3
Mathematics · #14F05 #14F17 #32S60 #55N25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1804.05014
openalex publication_date 2018/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.