Linear Shafarevich conjecture

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

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1545-1581
Number of pages37
JournalAnnals of Mathematics
Issue number3
StatePublished - 2012

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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