Mathematische Annalen

, Volume 356, Issue 3, pp 1183–1202

Okounkov bodies and toric degenerations

Authors

    • Department of MathematicsUniversity of Washington
    • Institut de Mathématiques de Jussieu
Article

DOI: 10.1007/s00208-012-0880-3

Cite this article as:
Anderson, D. Math. Ann. (2013) 356: 1183. doi:10.1007/s00208-012-0880-3
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Abstract

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.

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© Springer-Verlag Berlin Heidelberg 2012