4 problems

Global generation conjecture. One can choose $S$ and $M_S\in{\cal M}_S$ such that $X\subset S$ is the zero-locus of a regular section

Fujita's spannedness conjecture. The adjoint bundle $K+nL$ is spanned unless $L^n=1$.

Kawamata's conjecture. The locally free sheaf

Work over an algebraically closed field $k$ of characteristic zero. Let $X$ be a smooth projective variety of dimension $n$, let $x\in X$ be a point, and let $L$ be an ample line b…