  For a principal $\rmSU(n)$-bundle over a compact manifold of dimension
$2,3,4$, we determine the orbit types of the action of the gauge group on the
space of connections modulo pointed local gauge transformations. We find that
they are given by Howe subgroups of $\rmSU(n)$ for which a certain
characteristic equation is solvable. Depending on the base manifold, this
equation leads to a linear, bilinear, or quadratic Diophantine equation.
