6 problems

Let $X$ be a projective variety, and let $N^1(X)$ be its real Néron–Severi space. The volume function … is defined by the asymptotic growth of sections and has a big cone consistin…

Let $X$ be a smooth projective variety of dimension $d$, and let $\textnormal{Big}(X)$ denote its big cone. An open subset $U\subseteq\textnormal{Big}(X)$ is called “large” in the…

Let $X$ be a compact Kähler manifold, let $H^{1,1}(X,\mathbb{R})$ be its real $(1,1)$-cohomology space, and let $\mathcal{E}^{\circ}\subseteq H^{1,1}(X,\mathbb{R})$ denote the full…

Differentiability conjecture. The volume function $\operatorname{vol}(\cdot)$ is differentiable throughout the big cone of every compact Kähler manifold.

Let $k$ be a positive integer, and let a bounded body in ${\mathbb R}^{2k+1}$ have the property that the volume cut off by an affine hyperplane depends algebraically on the coordin…

Let $X$ be a Kähler manifold of dimension $n$. Let $\alpha$ be a big class and let $\beta$ be a pseudo-effective class. The notation $\langle \alpha^{n-1}\rangle$ denotes the posit…