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Okounkov bodies and toric degenerations

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Author(s): Dave Anderson

Publication date Created: 25 January 2010

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Abstract

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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Most cited references 2

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Degenerations of flag and Schubert varieties to toric varieties

N. Gonciulea, V. Lakshmibai (1996)

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Toric degenerations of Schubert varieties

Philippe Caldero (2002)

0 comments Cited 25 times – based on 0 reviews      Review now

Author and article information

Journal

Publication date Created: 25 January 2010

Publication date Updated: 2012-10-30

Article

ArXiV ID: 1001.4566

SO-VID: 7ba8ce18-f9e9-4198-afce-c12892a5dcc7

License:

http://arxiv.org/licenses/nonexclusive-distrib/1.0/

History

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ACM classes 14C20 (Primary), 14D06, 14M25, 52B20, 32M10, 14M15, 14M17 (Secondary)

Journal reference Math. Ann. 356 (2013), no. 3, 1183-1202

Comments v3: final version, some expository improvements in Section 5, to appear in Math. Ann

Categories math.AG math.CO

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