Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (1 of 3)
Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University
Orbifold Kähler groups and the Shafarevich conjecture for Hirzebruch’s covering surfaces with equal weights
Pages: 317 – 332
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.
Kähler orbifold, fundamental group, line arrangements
2010 Mathematics Subject Classification
14F35, 14J29, 32J27, 32Q30
This research was partially supported by ANR grant ANR-16-CE40-0011-01 HODGEFUN.
Received 28 November 2016
Accepted 4 July 2017
Published 15 June 2018