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. © 2013 The Author(s).
Okounkov bodies of finitely generated divisors
Lozovanu V.
2014-01-01
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. © 2013 The Author(s).
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