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!



moduli space of two-term complexes of vector bundles over a fixed variety
paper:Moduli spaces of holomorphic triples over compact Riemann surfaces


