  This paper investigates the geometry of 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 integer valued function f(x) is obtained with the following
properties. If X is a canonically polarized surface with canonical
singularities defined over an algebraically closed field of characteristic p>0
such that p>f(K_X^2) and X has a nontrivial global vector field, then X is
unirational and the algebraic fundamental group is trivial. 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.
  This paper is mathematically identical to the previous version. The reason
that the paper is replaced is in order to point out that this paper is a
generalization to the case of singular surfaces with canonical singularities of
the paper "Vector fields and moduli of canonically polarized surfaces in
positive characteristic" with reference arXiv:1710.03076 which treated only the
case of smooth surfaces. The results of this paper supercede the results of the
aforementioned paper making it obsolete.
