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arXiv · 2311.11042

A New Invariant of Lattice polytopes

Winfried Bruns·Takayuki Hibi
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Abstract

The maximal degree of monomials belonging to the unique minimal system of monomial generators of the canonical module $\omega(K[{\mathcal P}])$ of the toric ring $K[{\mathcal P}]$ defined by a lattice polytope ${\mathcal P}$ will be studied. It is shown that if ${\mathcal P}$ possesses an interior lattice point, then the maximal degree is at most ${\rm dim} {\mathcal P} - 1$, and that this bound is the best possible in general.

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Winfried Bruns, Takayuki Hibi. 2023-11-18. A New Invariant of Lattice polytopes. https://arxiv.org/abs/2311.11042

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