  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}.
