Projectivity conjecture for Bridgeland moduli spaces on Del Pezzo surfaces

Let $S$ be a Del Pezzo surface, and consider the program of constructing suitable hearts of Bridgeland stability conditions from exceptional collections and applying it to moduli spaces of Bridgeland semistable objects. Projectivity conjecture. The program of ,cite{ABCH} can be carried out on any Del Pezzo surface $S$, yielding projective moduli spaces ${\mathcal M}_\sigma(v)$. This would extend the known projectivity results for Bridgeland moduli spaces on $\mathbb{P}^2$ and the Del Pezzo surfaces treated in the paper to all Del Pezzo surfaces.