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arXiv · 1806.08413

Arithmetically nef line bundles

Dennis Keeler
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Abstract

Let $L$ be a line bundle on a scheme $X$, proper over a field. The property of $L$ being nef can sometimes be "thickened", allowing reductions to positive characteristic. We call such line bundles arithmetically nef. It is known that a line bundle $L$ may be nef, but not arithmetically nef. We show that $L$ is arithmetically nef if and only if its restriction to its stable base locus is arithmetically nef. Consequently, if $L$ is nef and its stable base locus has dimension $1$ or less, then $L$ is arithmetically nef.

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Dennis Keeler. 2018-06-21. Arithmetically nef line bundles. https://doi.org/10.1307/mmj/1596700818

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