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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

Henrik Seppänen
Mathematisches Institut, Georg-August-Universität, Bunsenstrasse 3-5, 37073 Göttingen, Germany

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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