6 problems

Greb–Wong–Höring–Peternell conjecture. The tangent bundle $d4af_X$ is nef, respectively big and nef, if and only if some canonical extension $Z_X$ of $X$ is Stein, respectively aff…

Let $M$ be a compact Kähler manifold with nef tangent bundle $T_M$, and let $Z_M$ be its canonical extension associated with a Kähler class. Fano criterion conjecture. The canonica…

Let $M$ be a compact Kähler manifold that is not uniruled, and let $Z_M$ be a canonical extension associated with a Kähler class on $M$. Torus quotient conjecture. If $Z_M$ is Stei…

Let $M$ be a compact Kähler manifold, and let $\alpha\in H^1(M,\Omega_M)$ be a Kähler class. Consider the extension … and the associated canonical extension … Here, $T_M$ is the ta…

Distributive-envelope adjoint conjecture. The distributive envelope constructions may be used to define a category in which the canonical extension for lattices is a left adjoint.

Canonical-extension conjecture. Mutatis mutandis, the canonical extension of an arbitrary bounded lattice may be obtained in the same manner by “forgetting the topology” at the lev…