Constructive exceptional bundles on ${\mathbb{P}}^3$

We give a complete classification of the Chern characters of constructive exceptional vector bundles on ${\mathbb{P}}^3$ analogous to the work of Drézet and Le Potier on ${\mathbb{P}}^2$, and using this classification prove that a constructive exceptional bundle $E$ on ${\mathbb{P}}^3$ with $\mu (E)\ge 0$ is globally generated.