Abundance for threefolds in positive characteristic when $ν=2$ (2307.03938v1)

Abstract: In this paper, we prove the abundance conjecture for threefolds over an algebraically closed field $k$ of characteristic $p > 3$ in the case of numerical dimension equals to $2$. More precisely, we prove that if $(X,B)$ be a projective lc threefold pair over $k$ such that $K_{X}+B$ is nef and $\nu(K_{X}+B)=2$, then $K_{X}+B$ is semiample.