Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector fields and moduli of canonically polarized surfaces in positive
  characteristic   This paper investigates the geometry of smooth canonically polarized surfaces
defined over a field of positive characteristic which have a nontrivial global
vector field, and the implications that the existence of such surfaces has in
the moduli problem of canonically polarized surfaces.
  In particular, an explicit real valued function f(x) is obtained such that if
$X$ is a smooth canonically polarized surface defined over an algebraically
closed field of characteristic p>0 such that $K_X^2 <f(p)$, then $X$ is
unirational and the order of its algebraic fundamental group is at most two. As
a consequence of this result, large classes of canonically polarized surfaces
are identified whose moduli stack is Deligne-Mumford, a property that does not
hold in general in positive characteristic.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex