Given $C$ a smooth, projective, algebraic curve, the Artin stack $Bun_{r,d}$ is smooth, irreducible (I think) of dimension $r^2(g1)$. I am interested in the Artin stack $M_{r,c}$ of vector bundles of given rank and Chern classes on a smooth, projective surface. Is it smooth, irreducible? Or at least, is it equidimensional? If yes, which is its dimension? Is it better to work with it or with the stack "parametrizing" coherent sheaves? Do you have any reference where this stack is studied?
