Oda's conjecture for reflexive polytopes: some special cases

Abstract

In this paper, we show that Oda's question holds for $n$-dimensional simplicial reflexive polytope $P$ and lattice polytope $Q$ containing the origin, when the vertex of $Q$ is either a vertex of $P$ or the origin, provided that $P$ has no more than $n+1$ lattice points on each facet and possesses unimodular triangulation. Then we prove Oda's question is true for any two facet unimodular polytopes whose matrix defining the facets has at most two non-zero entries in each row, and also true for any almost co-unimodular pair of reflexive polytopes.