Linear Shafarevich conjecture

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

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1545-1581
Number of pages37
JournalAnnals of Mathematics
Volume176
Issue number3
DOIs
StatePublished - 2012

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Uniformization
Linear Group
Fundamental Group
Hodge Theory
Universal Space
Covering Space

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Eyssidieux, P., Katzarkov, L., Pantev, T., & Ramachandran, M. (2012). Linear Shafarevich conjecture. Annals of Mathematics, 176(3), 1545-1581. https://doi.org/10.4007/annals.2012.176.3.4

Linear Shafarevich conjecture. / Eyssidieux, P.; Katzarkov, Ludmil; Pantev, T.; Ramachandran, M.

In: Annals of Mathematics, Vol. 176, No. 3, 2012, p. 1545-1581.

Research output: Contribution to journalArticle

Eyssidieux, P, Katzarkov, L, Pantev, T & Ramachandran, M 2012, 'Linear Shafarevich conjecture', Annals of Mathematics, vol. 176, no. 3, pp. 1545-1581. https://doi.org/10.4007/annals.2012.176.3.4
Eyssidieux, P. ; Katzarkov, Ludmil ; Pantev, T. ; Ramachandran, M. / Linear Shafarevich conjecture. In: Annals of Mathematics. 2012 ; Vol. 176, No. 3. pp. 1545-1581.
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