Linear Shafarevich conjecture

P. Eyssidieux; L. Katzarkov; T. Pantev; M. Ramachandran

doi:http://doi.org/10.4007/annals.2012.176.3.4

Linear Shafarevich conjecture

Pages 1545-1581 from Volume 176 (2012), Issue 3 by P. Eyssidieux, L. Katzarkov, T. Pantev, M. Ramachandran

Abstract

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.

Keywords

Higgs bundles, non-abelian Hodge theory

DOI

https://doi.org/http://doi.org/10.4007/annals.2012.176.3.4

2979857

zbMATH

06121648

Milestones

Received: 21 April 2009
Revised: 5 March 2012
Accepted: 11 April 2012
Published online: 1 November 2012