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big and nef line bundle

Proceedings of the Edinburgh Mathematical Society (1)

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The Augmented Base Locus in Positive Characteristic
Paolo Cascini, James McKernan, Mircea Mustaţǎ
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 1 / February 2014

Published online by Cambridge University Press:

19 December 2013, pp. 79-87
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Let L be a nef line bundle on a projective scheme X in positive characteristic. We prove that the augmented base locus of L is equal to the union of the irreducible closed subsets V of X such that L∣V is not big. For a smooth variety in characteristic 0, this was proved by Nakamaye using vanishing theorems.