A New Invariant of Lattice polytopes
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914677061058560 |
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| author | Bruns, Winfried Hibi, Takayuki |
| author_facet | Bruns, Winfried Hibi, Takayuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11042 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A New Invariant of Lattice polytopes Bruns, Winfried Hibi, Takayuki Commutative Algebra Combinatorics 52B20, 05E40 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. |
| title | A New Invariant of Lattice polytopes |
| topic | Commutative Algebra Combinatorics 52B20, 05E40 |
| url | https://arxiv.org/abs/2311.11042 |