Moduli Spaces of Stable Pairs in Donaldson-Thomas Theory

Let $(X,{\mathcal{O}}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{c}\mathrm{o}\mathrm{h}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct a coarse moduli space for $\delta$-semistable pairs $(\mathcal{E},\varphi )$ consisting of a coherent sheaf $\mathcal{E}$ and a homomorphism $\phi\colon $\mathcal{D}$\rightarrow $\mathcal{E}$$. We prove a chamber structure result and establish a connection to the moduli space of coherent systems constructed by Le Potier in \cite{LeP} and \cite{LeP2}.