7 problems

Let $X$ be a closed Kähler manifold of complex dimension $n$, with Kähler classes $alpha$ and $beta$. For a Kähler form $omega\in\beta$, a Kähler form $theta\in\alpha$ is a sub-sol…

Donaldson's conjecture. The J-equation is solvable under the assumption

Wall-chamber decomposition conjecture. There exists a locally finite collection of closed real submanifolds $W_\sigma$ of codimension one in the Kähler cone $\mathcal K_X$—meaning…

Let $(X,\alpha,\beta)$ be a compact Kähler manifold with two Kähler classes. Let $\zeta_{min}$ be its minimal J-slope and let $\mu$ be the J-slope of the triple. Minimal J-slope se…

Let $(X,\alpha,\beta)$ be a compact Kähler manifold with two Kähler classes, and let $\mathcal{T}\in\alpha$ be a solution of the singular J-equation. Let $\mathcal{E}_{\omega}$ den…

Let $X$ be an $n$-dimensional compact Kähler manifold with Kähler classes $alpha$ and $beta$. For a modification $pi:X'\to X$ and an effective $\mathbb{R}$-divisor $D$ such that…

Let $(M,\bomega)$ be a compact connected Ke4hler manifold of complex dimension $n$, with Ke4hler form $\bomega$ and a class $[\bchi_0]\bin H^{1,1}(M;\bmathbb{R})$. The J-equation i…