Linear Shafarevich conjecture


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.


P. Eyssidieux

Institut Fourier
Université Joseph Fourier

L. Katzarkov

Department of Mathematics
University of Miami
Miami, FL 33146
Universität Wien
1010 Wien

T. Pantev

Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab.
209 South 33rd Street
Philadelphia, PA 19104-6395

M. Ramachandran

Department of Mathematics
The State University of New York at Buffalo
Buffalo, NY 14260-2900