Classifying smooth lattice polytopes via toric fibrations.

A. DICKENSTEIN

Boston, USA

Conferencia; Seminario GASC; 2009

Northeastern University, USA

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 toricfibrations, 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. Joint work with Sandra di Rocco and Ragni Piene.