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arXiv:1001.4566 [math.AG]AbstractReferencesReviewsResources

Okounkov bodies and toric degenerations

Dave Anderson

Published 2010-01-25, updated 2012-10-30Version 3

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.

Comments: v3: final version, some expository improvements in Section 5, to appear in Math. Ann
Journal: Math. Ann. 356 (2013), no. 3, 1183-1202
Categories: math.AG, math.CO
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