Abstract
Given arbitrary integers d and r with \(d \ge 4\) and \(1 \le r \le d + 1\), a reflexive polytope \({\mathscr {P}}\subset {\mathbb R}^d\) of dimension d with \(\mathrm{depth}\,K[{\mathscr {P}}] = r\) for which its dual polytope \({\mathscr {P}}^\vee \) is normal will be constructed, where \(K[{\mathscr {P}}]\) is the toric ring of \({\mathscr {P}}\).
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Acknowledgements
We are very grateful to the anonymous referees for their insightful reports that led to significant improvements of the form of the paper. The second author was partially supported by Grant-in-Aid for JSPS Fellows 16J01549.
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Hibi, T., Tsuchiya, A. The depth of a reflexive polytope. Arch. Math. 113, 265–272 (2019). https://doi.org/10.1007/s00013-019-01333-6
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DOI: https://doi.org/10.1007/s00013-019-01333-6