We show that the Okounkov body of a big divisor with a finitely generated section ring is a rational simplex for an appropriate choice of flag; furthermore, when the ambient variety is a surface, the same holds for every big divisor. Under somewhat more restrictive hypotheses, we also show that the corresponding semi-group is finitely generated
Anderson, D., Küronya, A., Lozovanu, V. (2014). Okounkov Bodies of Finitely Generated Divisors. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014(9), 2343-2355 [10.1093/imrn/rns286].
Okounkov Bodies of Finitely Generated Divisors
Lozovanu, V
2014
Abstract
We show that the Okounkov body of a big divisor with a finitely generated section ring is a rational simplex for an appropriate choice of flag; furthermore, when the ambient variety is a surface, the same holds for every big divisor. Under somewhat more restrictive hypotheses, we also show that the corresponding semi-group is finitely generated
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