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arXiv · 1611.09178

Orbifold k\"ahler groups and the shafarevich conjecture for hirzebruch's covering surfaces with equal weights

Philippe Eyssidieux
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Abstract

This article is devoted to examples of (orbifold) K\"ahler 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.

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Philippe Eyssidieux. 2016-11-28. Orbifold k\"ahler groups and the shafarevich conjecture for hirzebruch's covering surfaces with equal weights. https://arxiv.org/abs/1611.09178

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