10 problems

Effective b-semiampleness conjecture. There is an integer $I=I(d)$ such that one can choose the diagram with $K_{X'}+\Delta'=\phi^*(K_X+\Delta)$, $I\mathbb M_{Y'}$ Cartier and free…

Let $(X,B)$ be an lc pair such that $K_X+B$ is a $Q$-Cartier divisor, and let $f:(X,B)\to Z$ be an lc-trivial fibration. Let ${\mathbf D}_{\mo}$ denote its moduli b-divisor. Effect…

Let $f:(Y,\Delta)\to X$ be a generically log canonical fibration, and let $\mathbf{N}$ be its moduli b-divisor on the total space, which is b-nef and relatively b-semiample. Shokur…

Let $f:(Y,\Delta)\to X$ be an lc-trivial fibration, and let $\mathbf{M}$ denote its moduli b-divisor. B-semiampleness conjecture. The moduli part should be the pullback of an ample…

Effective adjunction conjecture. The moduli b-divisor $\mathbf{M}$ is b-semi-ample.

Let $(X,D)$ be an klt (respectively, lc) pair with dimension $d$, and let $f:(X,D)\to Z$ be an lc-trivial fibration. An $\mathbb R$-b-divisor ${\bf M}$ is $\Gamma$-base-point free…

Let $X$ be a normal complex analytic variety in Fujiki's class $\mathcal C$, let $\Delta$ be a $\mathbb Q$-divisor such that $K_X+\Delta$ is $\mathbb Q$-Cartier, and let $f:X\to Y$…

Log canonical base conjecture. There is an effective $\mathbb R$-divisor $\Delta_Y$ on $Y$ such that $(Y,\Delta_Y)$ is log canonical and

Let $f:(X,\Delta)\to Y$ be an lc-trivial fibration and let $\pi:Y\to S$ be a proper morphism. Let $\mathbf M$ be the moduli part of $f$. The b-semi-ampleness conjecture. The moduli…

Let $f:X\to Y$ be a projective surjective morphism between normal projective varieties with connected fibers, and let $(X,B)$ be log canonical with $K_X+B\sim_{\mathbb Q,Y}0$. Let…