Relative augmented base loci on noetherian schemes

Yusuke Ushiro

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arXiv · 2306.07127

Relative augmented base loci on noetherian schemes

Yusuke Ushiro

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Abstract

Let $f:X \to S$ be a projective morphism of noetherian schemes and let $L$ be an invertible sheaf on $X$. We show that the relative augmented base locus of $L$ coincides with the relative exceptional locus of $L$. We also prove a semi-ampleness criterion in terms of the exceptional locus generalizing the result of Keel.

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Yusuke Ushiro. 2023-08-07. Relative augmented base loci on noetherian schemes. https://arxiv.org/abs/2306.07127

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