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PARTIALLY AMPLE LINE BUNDLES ON TORIC VARIETIES

Part of: Special varieties Cycles and subschemes

Published online by Cambridge University Press:  21 July 2015

NATHAN BROOMHEAD ,
JOHN CHRISTIAN OTTEM  and
ARTIE PRENDERGAST-SMITH
NATHAN BROOMHEAD
Affiliation:
Insitut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, Hannover 30167, Germany e-mail: [email protected]
JOHN CHRISTIAN OTTEM
Affiliation:
DPMMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK e-mail: [email protected]
ARTIE PRENDERGAST-SMITH
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK e-mail: [email protected]
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Abstract

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In this note we study properties of partially ample line bundles on simplicial projective toric varieties. We prove that the cone of q-ample line bundles is a union of rational polyhedral cones, and calculate these cones in examples. We prove a restriction theorem for big q-ample line bundles, and deduce that q-ampleness of the anticanonical bundle is not invariant under flips. Finally we prove a Kodaira-type vanishing theorem for q-ample line bundles.

MSC classification

Primary: 14M25: Toric varieties, Newton polyhedra
Secondary: 14C20: Divisors, linear systems, invertible sheaves
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 587 - 598
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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