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 $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $δ$. Using GIT we contruct a coarse moduli space for $δ$-semistable pairs $(\mathcal{E},ϕ)$ consisting of a coherent sheaf $\mathcal{E}$ and a homomorphism $ϕ\colon \mathcal{D}\rightarrow \mathcal{E}$. 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}.

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