# The Artin stack of vector bundles\ cohrent sheaves on a surface.

Given $C$ a smooth, projective, algebraic curve, the Artin stack $Bun_{r,d}$ is smooth, irreducible (I think) of dimension $r^2(g-1)$. 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?

-
Work with it for what purpose? The only reference I'd recommend that Google won't easily turn up is C. Simpson's papers "Moduli of Representations I, II". –  userN Jan 21 '11 at 18:31
I went to some lectures in Rome by Max Lieblich in which he discussed such stacks, and I know that some people TeXed notes. Perhaps if such a person is reading this, such a person might provide a link. –  Chris Brav Jan 22 '11 at 21:46
Thank you! Do you remember the name of this person? –  ginevra86 Jan 24 '11 at 17:17