Title: On global Okounkov bodies of spherical varieties,
Abstract: 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.