2024/08/29 by Benjamin Bakker, Bakker, Benjamin, Yohan Brunebarbe +3
Mathematics · #14C30 #14D07 #14D20 #14E20 #14F35 #32E05 #32Q30 #32U10 #53C43 #58A14 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2408.16441
openalex publication_date 2024/08/29 · openalex created_date 2024/09/22 · openalex updated_date 2026/08/01
We prove that the universal cover of a normal complex algebraic variety admitting a faithful complex representation of its fundamental group is an analytic Zariski open subset of a holomorphically convex complex space. This is a non-proper version of the Shafarevich conjecture. More generally we define a class of subset of the Betti stack for which the covering space trivializing the corresponding local systems has this property. Secondly, we show that for any complex local system V on a normal complex algebraic variety X there is an algebraic map f \colon X→ Y contracting precisely the subvarieties on which V is isotrivial.