Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field

Abstract

Let $k$ be an $F$-finite field containing an infinite perfect field of positive characteristic. Let $(X,\Delta )$ be a projective log canonical pair over $k$. In this note we show that, for a semi-ample divisor $D$ on $X$, there exists an effective $\mathbb{Q}$-divisor ${\Delta }^{\prime }{\sim }_{\mathbb{Q}}\Delta +D$ such that $(X,{\Delta }^{\prime })$ is log canonical if there exists a log resolution of $(X,\Delta )$.

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