5 problems

Let $X$ be a Fano manifold with Picard rank one. The tangent bundle $T_X$ is said to be $(-K_X)$-slope stable if every subsheaf has strictly smaller $(-K_X)$-slope than $T_X$. Isko…

Let $X$ be a Fano manifold, let $n=\dim X$, and define the $(-K_X)$-slope of a subsheaf $\mathcal{E}\subseteq T_X$ by … The tangent bundle has $(-K_X)$-slope $\mu(T_X)=(-K_X)^n/n$.…

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…

Let $M$ be a Kähler manifold and let $D$ be a reduced effective divisor. Consider the complement $M\setminus D$ and the slope stability condition obtained by replacing $c_1(K_M)$ i…

Let $(M,L)$ be a polarized projective manifold, let $Z\subset M$ be an analytic subvariety, and let $\mu_\lambda(\mathcal{O}_Z,L)$ denote its cohomological slope for…