2 problems

Let $X$ be a compact Kähler manifold of dimension $n$. Let $\mathrm{Psef}(X)$ be the pseudoeffective cone in $H^{1,1}(X,\mathbf{R})$, and let $\mathrm{Int}(\mathrm{Psef}(X)^\vee)$…

Let $X$ be a smooth Fano variety. For an integer $k\geq 1$, call $X$ $k$-Fano if its Chern characters $ch_s(X)$ are positive for $1\leq s\leq k$. Let $\Effc kX$ denote the cone of…