Global Generation of Adjoint Line Bundles on Projective $5$-folds

Fei Ye, Zhixian Zhu

Published 2014-05-04, updated 2016-12-02Version 2

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$. We show that $\mathcal{O}_X(K_X+L)$ is globally generated.