The augmented base locus of real divisors over arbitrary fields

Caucher Birkar

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arXiv · 1312.0239

The augmented base locus of real divisors over arbitrary fields

Caucher Birkar

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Abstract

We show that the augmented base locus coincides with the exceptional locus (i.e. null locus) for any nef $\mathbb{R}$-Cartier divisor on any scheme projective over a field (of any characteristic). Next we prove a semi-ampleness criterion in terms of the augmented base locus generalizing a result of Keel. We also study nef divisors with positive top intersection number, and discuss some problems related to augmented base loci of log divisors.

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Caucher Birkar. 2013-12-01. The augmented base locus of real divisors over arbitrary fields. https://arxiv.org/abs/1312.0239

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