2016/11/28 by Philippe Eyssidieux, Eyssidieux, Philippe
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1611.09178
openalex publication_date 2016/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is devoted to examples of (orbifold) Kähler groups from the perspective of the so-called Shafarevich conjecture on holomorphic convexity. It aims at pointing out that every quasi-projective complex manifold with an 'interesting' fundamental group gives rise to interesting instances of this long-standing open question. Complements of line arrangements are one of the better known classes of quasi-projective complex surfaces with an interesting fundamental group. We solve the corresponding instance of the Shafarevich conjecture partially giving a proof that the universal covering surface of a Hirzebruch's covering surface with equal weights is holomorphically convex. The final section reduces the Shafarevich conjecture to a question related to the Serre problem.