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 exceptional locus generalizing a result of Keel. We also discuss some problems related to augmented base loci of log divisors.

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