MINKOWSKI DECOMPOSITION AND GENERATORS OF THE MOVING CONE FOR TORIC VARIETIES:

Abstract

We prove that for smooth projective toric varieties, the Okounkov body of a |$T$|-invariant pseudo-effective divisor with respect to a |$T$|-invariant flag decomposes as a finite Minkowski sum of indecomposable polytopes, and that the set of these polytopes corresponds to a finite Minkowski basis whose elements span the extremal rays in the secondary fan. In fact, the Minkowski basis does not depend on the choice of the |$T$|-invariant flag. Moreover, we present an algorithm that computes the Minkowski basis.

Locations

• arXiv (Cornell University) - View - PDF
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• The Quarterly Journal of Mathematics - View