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?
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$\begingroup$ 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". $\endgroup$– user1504Commented Jan 21, 2011 at 18:31
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$\begingroup$ 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. $\endgroup$– Chris BravCommented Jan 22, 2011 at 21:46
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$\begingroup$ Thank you! Do you remember the name of this person? $\endgroup$– ginevra86Commented Jan 24, 2011 at 17:17
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