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arXiv · 1209.3128

Metrics on universal covering of projective variety

Robert Treger
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Abstract

Let U be a universal covering of a connected nonsingular projective variety X with large and residually finite fundamental group. We construct metrics on U and provide another version of the uniformization theorem, namely: if the fundamental group of X is, in addition, nonamenable then U is a bounded Stein domain. The Appendix contains a proof of the Shafarevich conjecture provided the fundamental group is residually finite.

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Robert Treger. 2012-09-14. Metrics on universal covering of projective variety. https://arxiv.org/abs/1209.3128

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