On the fundamental group of hyperelliptic fibrations and some applications

• 成果类型: Article
• 署名作者: Gurjar, R. V.; Paul, S.; Purnaprajna, B. P.
• 署名单位: Tata Institute of Fundamental Research (TIFR); University of Kansas
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0318-7
• 发表日期: 2011
• 页码: 237-254
• 关键词: conjecture

摘要

We prove that for a hyperelliptic fibration on a surface of general type with irreducible fibers over a (possibly) non-complete curve, the image of the fundamental group of a general fiber in the fundamental group of the surface is finite. Examples show that the result is optimal. As a corollary of this result we prove two conjectures; the Shafarevich conjecture on holomorphic convexity for the universal cover of these surfaces, and a conjecture of Nori on the finiteness of the fundamental groups of some surfaces. We also prove a striking general result about the multiplicities of multiple fibers of a hyperelliptic fibration on a smooth, projective surface.