Perverse sheaves on semi-abelian varieties—a survey of properties and applications

  • Yongqiang Liu
  • Laurentiu MaximEmail author
  • Botong Wang
Research/Review Article


We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various restrictions on the homotopy type of complex algebraic manifolds (expressed in terms of their cohomology jump loci), homological duality properties of complex algebraic manifolds, as well as new topological characterizations of semi-abelian varieties.


Semi-abelian variety Perverse sheaf Mellin transformation Cohomology jump loci Albanese map Generic vanishing Abelian duality space 

Mathematics Subject Classification

32S60 14F17 14F05 55N25 



We would like to thank the organizers of the conference Topology and Geometry: A conference in memory of Ştefan Papadima (Bucharest, Romania, May 2018), where part of this work was presented.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.BCAM - Basque Center for Applied MathematicsBilbaoSpain
  2. 2.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

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