Integer decomposition property of polytopes

Abstract

We study the integer decomposition property of lattice polytopes associated with the $n$-dimensional smooth complete fans with at most $n+3$ rays. Using the classification of smooth complete fans by Kleinschmidt and Batyrev and a reduction to lower dimensional polytopes, we prove the integer decomposition property for lattice polytopes in this setting.

V2, the exposition of the proof of Theorem 1.4 has improved