Journal of Lie Theory 29 (2019), No. 4, 1031--1044
Copyright Heldermann Verlag 2019
On Global Okounkov Bodies of Spherical Varieties
Guido Pezzini
Dip. di Matematica "G. Castelnuovo", Universitā "La Sapienza", Piazzale A. Moro 5, 00185 Roma, Italy
pezzini@mat.uniroma1.it
Henrik Seppänen
Mathematisches Institut, Georg-August-Universität, Bunsenstrasse 3-5, 37073 Göttingen, Germany
henrik.seppaenen@mathematik.uni-goettingen.de
We define and study the global Okounkov moment cone of a projective spherical variety X, generalizing both the global Okounkov body and the moment body of X defined by Kaveh and Khovanskii. Under mild assumptions on X we show that the global Okounkov moment cone of X is rational polyhedral. As a consequence, also the global Okounkov body of X, with respect to a particular valuation, is rational polyhedral.
Keywords: Spherical varieties, Newton-Okounkov bodies.
MSC: 14C20, 14M27.
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