Mathematische Annalen

, Volume 356, Issue 3, pp 1183–1202

Okounkov bodies and toric degenerations



Let \(\varDelta \) be the Okounkov body of a divisor \(D\) on a projective variety \(X\). We describe a geometric criterion for \(\varDelta \) 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Institut de Mathématiques de JussieuParisFrance

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