Classifying smooth lattice polytopes via toric fibrations

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We define Q-normal lattice polytopes. Natural examples of such polytopes are Cayley sums of strictly combinatorially equivalent lattice polytopes, which correspond to particularly nice toric fibrations, namely toric projective bundles. In a recent paper Batyrev and Nill have suggested that there should be a bound, N(d), such that every lattice polytope of degree d and dimension at least N(d) decomposes as a Cayley sum. We give a sharp answer to this question for smooth Q-normal polytopes. We show that any smooth Q-normal lattice polytope P of dimension n and degree d is a Cayley sum of strictly combinatorially equivalent polytopes if n is greater than or equal to 2d+1. The proof relies on the study of the nef value morphism associated to the corresponding toric embedding.
Revised version, minor changes. To appear in Advances in Math

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Algebraic Geometry, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/225211

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.3136
 http://arxiv.org/abs/0809.3136

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arXiv