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The Augmented Base Locus in Positive Characteristic

Published online by Cambridge University Press:  19 December 2013

Paolo Cascini ,
James McKernan  and
Mircea Mustaţǎ
Paolo Cascini
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK (p.cascini@imperial.ac.uk)
James McKernan
Affiliation:
Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA (mckernan@math.mit.edu)
Mircea Mustaţǎ
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA (mmustata@umich.edu)
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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 L∣V is not big. For a smooth variety in characteristic 0, this was proved by Nakamaye using vanishing theorems.

Keywords

stable base locusaugmented base locusbig and nef line bundlePrimary 14A15Secondary 14E99
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 79 - 87
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

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