11 problems

Let $X$ be a smooth projective variety and let $K_X$ be its canonical bundle. The canonical ring of $X$ is … It is a birational invariant of $X$. Finite generation conjecture. For…

Let $X$ be a compact complex manifold. Its canonical ring is the graded $4\mathbb C4$-algebra … where $4\mathbb C=H^0(X,\mathcal O_X)4$. Canonical ring finite generation conjecture…

Finite-generation conjecture. The canonical ring $R(X,K_X)$ is finitely generated.

Soit $(X,\Delta)$ une paire projective à singularités log canoniques, et soit son algèbre canonique … où $\left\lfloor l\Delta\right\rfloor$ est le diviseur de Weil obtenu en arron…

Let $X_n$ denote the locus of configurations $(P_1,\ldots,P_n)$ for which the canonical ring has exceptional generation behavior, and let the fat diagonal be the locus where at lea…

Let $D$ be a … , supported at points $P_1,,P_n$, and let $S_D$ be its canonical ring. A minimal relation means a relation in a minimal presentation of $S_D$ by generators. The poin…

Fujiki-class finite-generation conjecture. The ring $R(X,\Delta)$ is a finitely generated $\mathbb C$-algebra. The source states that this conjecture is equivalent, after taking a…

Finite-generation conjecture. The ring $R(X,\Delta)$ is a finitely generated $\mathbb C$-algebra. The surrounding discussion distinguishes this conjecture from the established klt…

3-connectedness conjecture. If $K_S$ is 3-connected, then $R(S,K_S)$ should be generated by elements of degrees $1$, $2$, and $3$, at least when $q=0$.

Canonical ring finite-generation conjecture. The canonical ring $R(X,K_X+\Delta)$ is finitely generated.

Finite-generation conjecture. The sheaf $\bigoplus_{m\geq 0}\mathcal{O}_X(mK_X)$ is a finitely generated sheaf of $\mathcal{O}_X$-algebras.