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arxiv: 1001.4566 · v3 · pith:5TTUHYZKnew · submitted 2010-01-25 · 🧮 math.AG · math.CO

Okounkov bodies and toric degenerations

classification 🧮 math.AG math.CO
keywords degenerationdeltaokounkovtoricvarietyadmitsappropriatebodies
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Let \Delta be the Okounkov body of a divisor D on a projective variety X. We describe a geometric criterion for \Delta to 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.

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