The augmented base locus of real divisors over arbitrary fields

By C. Birkar. 2013

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

Subfields: Applied Mathematics, Geometry and Topology, Rehabilitation

View Paper: https://www.semanticscholar.org/paper/21146a3a47c11581033ae047641b3ac0b7985a13