9 problems

Fujita's Spectrum Conjecture. For every $\varepsilon>0$, the set

Strong saturation conjecture. The complex analytic variety $V({\bf C})$ is ${\cal L}$-primitive.

Polyhedrality conjecture. The cone $\Lambda_{\rm eff}(V,{\cal L})$ is a rational finitely generated polyhedral cone.

Rationality conjecture. If

Uniformizability conjecture. The stack $\mathcal{M}_h$ is uniformizable by a quasi-projective scheme over $\mathbb{Q}$. Uniformizability would allow finiteness results proved for s…

The Yau–Tian–Donaldson conjecture for maps. The class $c_1(L)$ admits a $p^*\alpha$-twisted cscK metric if and only if the map $p:(X,L)\to(Y,T)$ is uniformly K-stable. This is the…

Let $(X,L)$ be a quasi polarized manifold of dimension $n$, meaning that $X$ is a projective manifold and $L$ is a nef and big Cartier divisor. Let $s>0$. Effective adjunction thre…

Let $(X,L)$ be a projective variety of dimension $n$ with at most terminal $\mathbb{Q}$-factorial singularities, where $L$ is a nef and big Cartier divisor; such a pair $(X,L)$ is…

Let $(X,\mathcal{L})$ be a polarized manifold of dimension $n\geq 3$. For each integer $i$ with $2\leq i\leq n-1$, let $K_X$ denote the canonical divisor, let $g_i(X,\mathcal{L})$…