Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolicity and uniformity of varieties of log general type   Projective varieties with ample cotangent bundle satisfy many notions of
hyperbolicity, and one goal of this paper is to discuss generalizations to
quasi-projective varieties. A major hurdle is that the naive generalization
fails, i.e. the log cotangent bundle is never ample. Instead, we define a
notion called almost ample which roughly asks that the log cotangent is as
positive as possible. We show that all subvarieties of a quasi-projective
variety with almost ample log cotangent bundle are of log general type. In
addition, if one assumes globally generated then we obtain that such varieties
contain finitely many integral points. In another direction, we show that the
Lang-Vojta conjecture implies the number of stably integral points on curves of
log general type, and surfaces of log general type with almost ample log
cotangent sheaf are uniformly bounded.

26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio