Full Exceptional Sequence for a Fine Quiver Moduli Space

We consider the fine quiver moduli space of representations of the 3-Kronecker quiver of dimension vector $(2,3)$, which is a blow down of the Hilbert scheme of 3 points on $\text{mathds}{P}^2$. A short description of its geometry and Chow ring is given. Then we exhibit an exceptional sequence for the derived category by understanding a $\text{mathds}{P}^1$-bundle over it and using Teleman Quantization. The fullness of the exceptional sequence is proved by using a covering argument and computations of mutations.