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arXiv · 1607.03667

On numerical Newton-Okounkov bodies and the existence of Minkowski bases

William F. Sawin·David Schmitz
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Abstract

Towards the boundary of the big cone, Newton-Okounkov bodies do not vary continuously and in fact the body of a boundary class is not well defined. Using the global Okounkov body one can nonetheless define a numerical invariant, the numerical Newton-Okounkov body. We show that if a normal projective variety has a rational polyhedral global Okounkov body, it admits a Minkowski basis provided one includes numerical Newton-Okounkov bodies above non-big classes. Under the same assumption, we also show that the dimension of the numerical Newton-Okounkov body is the numerical Kodaira dimension.

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William F. Sawin, David Schmitz. 2016-07-13. On numerical Newton-Okounkov bodies and the existence of Minkowski bases. https://arxiv.org/abs/1607.03667

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