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The Augmented Base Locus in Positive Characteristic

Published online by Cambridge University Press:  19 December 2013

Paolo Cascini
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK ([email protected])
James McKernan
Affiliation:
Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA ([email protected])
Mircea Mustaţǎ
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA ([email protected])
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Abstract

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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 LV is not big. For a smooth variety in characteristic 0, this was proved by Nakamaye using vanishing theorems.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

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