Okounkov bodies of finitely generated divisors

Dave, Anderson and Küronya, Alex and Victor, Lozovanu (2014) Okounkov bodies of finitely generated divisors. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014 (9). pp. 2343-2355. ISSN 1073-7928

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Abstract

We show that the Okounkov body of a big divisor with 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 semigroup is finitely generated.

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