2 problems

Let $(X,B)$ be a log minimal model with $\dim(X)=4$, and let $C$ be a very general curve in $X$. Four-dimensional numerical non-vanishing conjecture. If $(K+B)\cdot C>0$ for very g…

Let $(X,B)$ be a complex projective log variety with Kawamata log terminal singularities such that $K+B$ is nef. For a positive integer $m$, write $|m(K+B)|$ for the pluricanonical…