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Local positivity of
linear series on surfaces
Alex Küronya and Victor Lozovanu |
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Vol. 12 (2018), No. 1, 1–34
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Abstract |
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We study asymptotic invariants of linear series on surfaces with the help of Newton–Okounkov polygons. Our primary aim is to understand local positivity of line bundles in terms of convex geometry. We work out characterizations of ample and nef line bundles in terms of their Newton–Okounkov bodies, treating the infinitesimal case as well. One of the main results is a description of moving Seshadri constants via infinitesimal Newton–Okounkov polygons. As an illustration of our ideas we reprove results of Ein–Lazarsfeld on Seshadri constants on surfaces. |
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Keywords
Newton–Okounkov bodies, linear series on surfaces, local
positivity
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Mathematical Subject Classification 2010
Primary: 14C20
Secondary: 14J99, 32Q15, 52B99
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Milestones
Received: 30 May 2016
Revised: 7 April 2017
Accepted: 13 May 2017
Published: 13 March 2018
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Authors |
| Alex Küronya | |
| Institut für Mathematik Johann-Wolfgang-Goethe Universität Frankfurt D-60325 Frankfurt am Main Germany |
Budapest University of Technology
and Economics Department of Algebra H-1111 Budapest Hungary |
| Victor Lozovanu | |
| Institut für Algebraische
Geometrie Leibniz Universität Hannover D-30167 Hannover Germany |
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