  Suppose $S$ is a smooth projective surface over an algebraically closed field
$k$, $\mathcal{L}=\{L_1,\ldots,L_n\}$ is a full strong exceptional collection
of line bundles on $S$. Let $Q$ be the quiver associated to this collection.
One might hope that $S$ is the moduli space of representations of $Q$ with
dimension vector $(1,\ldots,1)$ for a suitably chosen stability condition
$\theta$: $S\cong M_\theta$. In this paper, we show that this is the case for
del Pezzo surfaces. Furthermore, we show the blow-up at a point can be
recovered from an augmentation of exceptional collections (in the sense of L.
Hille and M.Perling) via morphism between moduli of quiver representations.
