The depth of a reflexive polytope

Abstract

Given arbitrary integers $d$ and $r$ with $d\ge 4$ and $1\le r\le d+1$, a reflexive polytope $\mathcal{P}\subset {\mathbb{R}}^d$ of dimension $d$ with $\mathrm{depth}K[\mathcal{P}]=r$ for which its dual polytope ${\mathcal{P}}^{\vee }$ is normal will be constructed, where $K[\mathcal{P}]$ is the toric ring of $\mathcal{P}$.

7 pages, to appear in Archiv der Mathematik