A New Invariant of Lattice polytopes

2023/11/18 by Bruns, Winfried, Hibi, Takayuki · 1 citation
#05E40 #52B20 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.11042

Abstract

The maximal degree of monomials belonging to the unique minimal system of monomial generators of the canonical module ω(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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