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I want to get some practice and build more appreciation for the use of stacks in the context of classical moduli spaces of sheaves. Here by classical I vaguely mean hands-on description of the geometry of moduli spaces of sheaves in the spirit of work of Drézet-Le Potier and the book of Huybrechts-Lehn. Two great papers I've read so far which use stacky techniques are Walter's "Irreducibility of moduli spaces of vector bundles on birationally ruled surfaces" and Göttsche-Hirschowitz's "Weak Brill-Noether for vector bundles on the projective plane".

Can you recommend me more great papers using stacks to prove things about moduli spaces of sheaves?

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    $\begingroup$ My advisor Izzet Coskun has, with various collaborators, published extensively about moduli spaces of sheaves, mostly on various rational surfaces, in the last 7 years or so. I would look at the papers on his website. I can't really wrap my head around this stuff, but I know that the stack of prioritary sheaves often comes up in the proofs. $\endgroup$ Jul 21, 2019 at 21:16
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    $\begingroup$ @TabesBridges, thank you for your comment. I am very familiar with Izzet's techniques and as far as I know he and his collaborators mostly build on geometric properties of that stack proved by Walter in the paper I mentioned above. $\endgroup$
    – Bananeen
    Jul 21, 2019 at 21:51
  • $\begingroup$ Ah OK, thanks for the info. $\endgroup$ Jul 22, 2019 at 0:51

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