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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Acknowledgments
I would like to thank Mircea Mustaţă and Karl Schwede for discussions related to Sect. 6, and thank the referee for the valuable comments and corrections. This work was supported by a grant of the Leverhulme Trust.
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Communicated by Ngaiming Mok.