Okounkov bodies and toric degenerations
arXiv:1001.4566
Abstract
Let Δbe the Okounkov body of a divisor D on a projective variety X. We describe a geometric criterion for Δto be a lattice polytope, and show that in this situation X admits a flat degeneration to the corresponding toric variety. This degeneration is functorial in an appropriate sense.
v3: final version, some expository improvements in Section 5, to appear in Math. Ann
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