Local positivity in terms of Newton-Okounkov bodies
Roé Vellvé, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	In recent years, the study of Newton-Okounkov bodies on normal varieties has become a central subject in the asymptotic theory of linear series, after its introduction by Lazarsfeld-Mustata and Kaveh-Khovanskii. One reason for this is that they encode all numerical equivalence information of divisor classes (by work of Jow). At the same time, they can be seen as local positivity invariants, and Küronya-Lozovanu have studied them in depth from this point of view. We determine what information is encoded by the set of all Newton-Okounkov bodies of a big divisor with respect to flags centered at a fixed point of a surface, by showing that it determines and is determined by the numerical equivalence class of the divisor up to negative components in the Zariski decomposition that do not go through the fixed point.
Note:	Agraïments: The author greatly benefited from conversations with A. Küronya on the contents of this work.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Newton-Okounkov body ; Linear system ; Big divisor ; Positivity ; Local positivity ; Algebraic geometry ; Algebraic surface
Published in:	Advances in mathematics, Vol. 301 (2016) , p. 486-498, ISSN 1090-2082

DOI: 10.1016/j.aim.2016.05.028

Post-print 11 p, 138.4 KB

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