Classifying smooth lattice polytopes via toric fibrations
| dc.creator | Dickenstein, Alicia | |
| dc.creator | Di Rocco, Sandra | |
| dc.creator | Piene, Ragni | |
| dc.date | 2008-09-18 | |
| dc.date | 2009-04-01 | |
| dc.date.accessioned | 2026-07-07T12:58:20Z | |
| dc.date.available | 2026-07-07T12:58:20Z | |
| dc.description | 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. | |
| dc.description | Revised version, minor changes. To appear in Advances in Math | |
| dc.identifier | https://arxiv.org/abs/0809.3136 | |
| dc.identifier | http://arxiv.org/abs/0809.3136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225211 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.title | Classifying smooth lattice polytopes via toric fibrations | |
| dc.type | text |