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

Abstract

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 $L^d\cdot Z\ge 7^d$ for any subvariety $Z$ of dimension $1\le d\le 4$. We show that ${\mathcal{O}}_X(K_X+L)$ is globally generated.

arXiv commentFinal version to appear in manuscripta mathematica. We notice that mistakes were introduced by the journal to some fractions in the form "expression/expression" which should be read as "(expression)/(expression)"