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.

Küronya, A., Lozovanu, V. (2014). Local positivity of linear series on surfaces [Working paper].

Local positivity of linear series on surfaces

LOZOVANU, VICTOR
Ultimo
2014

Abstract

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.
Working paper
Mathematics - Algebraic Geometry; Mathematics - Algebraic Geometry; Mathematics - Complex Variables; 14C20, 14J99 (primary), 52B99, 32Q15 (secondary)
English
2014
http://arxiv.org/abs/1411.6205v1
Küronya, A., Lozovanu, V. (2014). Local positivity of linear series on surfaces [Working paper].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/62174
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