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arXiv · 1805.12446

The depth of a reflexive polytope

Takayuki Hibi·Akiyoshi Tsuchiya
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Abstract

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

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Takayuki Hibi, Akiyoshi Tsuchiya. 2019-04-15. The depth of a reflexive polytope. https://doi.org/10.1007/s00013-019-01333-6

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