Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

4 Issues per year


IMPACT FACTOR 2017: 0.734

CiteScore 2017: 0.70

SCImago Journal Rank (SJR) 2017: 0.695
Source Normalized Impact per Paper (SNIP) 2017: 0.891

Mathematical Citation Quotient (MCQ) 2017: 0.62

Online
ISSN
1615-7168
See all formats and pricing
More options …
Volume 16, Issue 1

Issues

On the polyhedrality of global Okounkov bodies

David Schmitz
  • Corresponding author
  • Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, 35032 Marburg, Germany
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Henrik Seppänen
Published Online: 2016-01-16 | DOI: https://doi.org/10.1515/advgeom-2015-0042

Abstract

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.

Export Citation

© 2016 by Walter de Gruyter Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
David Schmitz and Henrik Seppänen
Journal of Algebra, 2017, Volume 490, Page 518
[2]
Henrik Seppänen
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016, Volume 57, Number 4, Page 735

Comments (0)

Please log in or register to comment.
Log in