3 problems

Let $e\geq 2$ and let $\mathcal{V}$ be an exceptional bundle on the Hirzebruch surface $\mathbb{F}_e$. Small-polarization stability conjecture. The bundle $\mathcal{V}$ is…

Extremal-pair conjecture. Every $\xi$ above the Rudakov $\delta$-surface has an extremal pair, and every controlling exceptional bundle of an extremal pair is contained in two extr…

Let $Y$ be a smooth projective surface such that $K_Y$ is ample, $H^2(\mathcal T_Y)=0$, $H^{2,0}(Y)=0$, and $\pi_1(Y)=0$. Let $S$ be the set of slope vectors…