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

TL;DR

This survey reviews recent advances in understanding perverse sheaves on semi-abelian varieties, highlighting their applications in topology, cohomology, and duality properties of complex algebraic manifolds.

Contribution

It compiles recent results on the properties and applications of perverse sheaves on semi-abelian varieties, emphasizing new topological and homological insights.

Findings

Obstructions on homotopy types via cohomology jump loci

Homological duality properties of complex algebraic manifolds

Topological characterizations of semi-abelian varieties

Abstract

We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various obstructions 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.