Bridgeland Stability of Sheaves on del Pezzo Surface of Picard Rank Three

This article discusses the Bridgeland stability of some sheaves on the blow-up of ${\mathbb{P}}^2$ at two general points. We have determined the destabilizing objects of the line bundles and have shown that $\mathcal{O}(E){\mathrm{\mid }}_E$ is Bridgeland stable for any $(-1)$-curve $E$ and any divisorial Bridgeland stability condition.