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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 16, Issue 1


On the polyhedrality of global Okounkov bodies

David Schmitz
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  • Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, 35032 Marburg, Germany
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/ Henrik Seppänen
Published Online: 2016-01-16 | DOI: https://doi.org/10.1515/advgeom-2015-0042


We prove that the existence of a finite Minkowski basis for Okounkov bodies on a smooth projective variety with respect to an admissible flag implies the rational polyhedrality of the global Okounkov body. As an application of this general result, we deduce that the global Okounkov body of a surface with finitely generated pseudo-effective cone with respect to a general flag is rational polyhedral. We give an alternative proof for this fact which recovers the generators more explicitly. We also prove the rational polyhedrality of global Okounkov bodies in the case of certain homogeneous 3-folds using inductive methods.

Keywords: Okounkov body; Minkowski basis; chamber decomposition

About the article

Received: 2014-06-17

Revised: 2014-07-09

Published Online: 2016-01-16

Published in Print: 2016-01-01

Citation Information: Advances in Geometry, Volume 16, Issue 1, Pages 83–91, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0042.

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David Schmitz and Henrik Seppänen
Journal of Algebra, 2017, Volume 490, Page 518
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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016, Volume 57, Number 4, Page 735

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