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Let $X$ be a fixed algebraic manifold over $\mathbb{C}$ , $\{E_{a}\}$ be vector bundles over $X$. We can construct moduli space of $\{E_{a}\}$ by classical theory. My question is that if we consider the category $\mathcal{C}$ of two-term complexes$\{E_1 \xrightarrow{\phi} E_2\}$ where $E_1,E_2$ are vector bundles over $X$ and $\phi$ is homomorphism between bundles. How to define the equivalence relation of two objects of $\mathcal{C}$ and construct moduli space of $\mathcal{C}$ (if we can) ?

I heard that there is some results on GIT construction of complexes and recent progress on derived objects. Who can tell me where I can find some useful results (in some papers)? Thank you!

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paper:Moduli spaces of holomorphic triples over compact Riemann surfaces

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    $\begingroup$ Providing complete references (at least the authors!) is somewhat more scholarly... $\endgroup$
    – Mariano Suárez-Álvarez
    Commented Oct 25, 2013 at 7:09
  • $\begingroup$ arxiv.org/abs/math/0211428v2 Steven B. Bradlow , Oscar Garcia-Prada , Peter B. Gothen $\endgroup$
    – swalker
    Commented Oct 26, 2013 at 4:25
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    $\begingroup$ You can edit your answer and add the information there. $\endgroup$
    – Mariano Suárez-Álvarez
    Commented Oct 26, 2013 at 4:29

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