A new invariant of lattice polytopes
DOI:
https://doi.org/10.7146/math.scand.a-143486Abstract
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 $\dim \mathcal{P} - 1$, and that this bound is the best possible in general.
References
Bruns, W., and Gubeladze, J., Polytopes, rings, and $K$-theory, Springer Monographs in Mathematics. Springer, Dordrecht, 2009. https://doi.org/10.1007/b105283
Bruns, W., Gubeladze, J., Trung, N. V., Normal polytopes, triangulations, and Koszul algebras, J. Reine Angew. Math. 485 (1997), 123–160.
Bruns, W., Ichim, B., Söger, C., and von der Ohe, U., Normaliz, Algorithms for rational cones and affine monoids. Available at https://www.normaliz.uni-osnabrueck.de.
Herzog, J., and Hibi, T., Discrete polymatroids, J. Algebraic Combin. 16 (2002), no. 3, 239–268 https://doi.org/10.1023/A:1021852421716
Hibi, T., Algebraic combinatorics on convex polytopes, Carslaw Publications, Glebe, N.S.W., Australia, 1992.
