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 $\delta$. Using GIT we contruct a coarse moduli space for $\delta$-semistable pairs $(\mathcal{ E},\phi)$ 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}.
Categories: math.AG