Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metrics on universal covering of projective variety   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.

22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex