Geodesic
Linear Shafarevich conjecture
P. Eyssidieux1 ; L. Katzarkov2 ; T. Pantev3 ; M. Ramachandran4
1 Institut Fourier<br/> Université Joseph Fourier<br/>Grenoble <br/> France
2 Department of Mathematics<br/> University of Miami<br/> Miami, FL 33146 <br/> and <br/> Universität Wien<br/> 1010 Wien<br/> Austria
3 Department of Mathematics<br/> University of Pennsylvania<br/> David Rittenhouse Lab.<br/> 209 South 33rd Street<br/> Philadelphia, PA 19104-6395
4 Department of Mathematics<br/> The State University of New York at Buffalo<br/> Buffalo, NY 14260-2900
Annals of mathematics, Tome 176 (2012) no. 3, pp. 1545-1581.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2012.176.3.4

P. Eyssidieux 1 ; L. Katzarkov 2 ; T. Pantev 3 ; M. Ramachandran 4

1 Institut Fourier<br/> Université Joseph Fourier<br/>Grenoble <br/> France
2 Department of Mathematics<br/> University of Miami<br/> Miami, FL 33146 <br/> and <br/> Universität Wien<br/> 1010 Wien<br/> Austria
3 Department of Mathematics<br/> University of Pennsylvania<br/> David Rittenhouse Lab.<br/> 209 South 33rd Street<br/> Philadelphia, PA 19104-6395
4 Department of Mathematics<br/> The State University of New York at Buffalo<br/> Buffalo, NY 14260-2900 
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     title = {Linear {Shafarevich} conjecture},
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P. Eyssidieux; L. Katzarkov; T. Pantev; M. Ramachandran. Linear Shafarevich conjecture. Annals of mathematics, Tome 176 (2012) no. 3, pp. 1545-1581. doi : 10.4007/annals.2012.176.3.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.4/

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