Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite volume complex-hyperbolic surfaces, their toroidal
  compactifications, and geometric applications   We study the classification of smooth toroidal compactifications of
nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover,
several results concerning the Riemannian and complex algebraic geometry of
these spaces are given. In particular we show that there are compact complex
surfaces which admit Riemannian metrics of nonpositive curvature, but which do
not admit K\"ahler metrics of nonpositive curvature. An infinite class of such
examples arise as smooth toroidal compactifications of ball quotients.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph