Linear Shafarevich conjecture

• 成果类型: Article
• 署名作者: Eyssidieux, P.; Katzarkov, L.; Pantev, T.; Ramachandran, M.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.176.3.4
• 发表日期: 2012
• 页码: 1545-1581
• 关键词: universal coverings; vector-bundles; REPRESENTATIONS; convexity; SPACES; MODULI; MAPS

摘要

In this paper we settle affirmatively Shafarevich's uniformization conjecture for varieties with linear fundamental groups. We prove the strongest to date uniformization result - the universal covering space of a complex projective manifold with a linear fundamental group is holomorphically convex. The proof is based on both known and newly developed techniques in non-abelian Hodge theory.