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

2016/07/13 by Sawin, William F., Schmitz, David
#14C20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.03667

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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