Minimal free resolutions of numerical semigroup algebras via Apéry specialization
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929707968102400 |
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| author | Braun, Benjamin Gomes, Tara Miller, Ezra O'Neill, Christopher Sobieska, Aleksandra |
| author_facet | Braun, Benjamin Gomes, Tara Miller, Ezra O'Neill, Christopher Sobieska, Aleksandra |
| contents | Numerical semigroups with multiplicity $m$ are parameterized by integer points in a polyhedral cone $C_m$, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall structure is identical for all semigroups parametrized by the relative interior of a fixed face of $C_m$. The matrix entries of this resolution are monomials whose exponents are parametrized by the coordinates of the corresponding point in $C_m$, and minimality of the resolution is achieved when the semigroup is maximal embedding dimension, which is the case parametrized by the interior of $C_m$ itself. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_03612 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal free resolutions of numerical semigroup algebras via Apéry specialization Braun, Benjamin Gomes, Tara Miller, Ezra O'Neill, Christopher Sobieska, Aleksandra Commutative Algebra Combinatorics 20M14, 13D02, 52B05 (Primary), 05E40, 13F20, 13F65 (Secondary) Numerical semigroups with multiplicity $m$ are parameterized by integer points in a polyhedral cone $C_m$, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall structure is identical for all semigroups parametrized by the relative interior of a fixed face of $C_m$. The matrix entries of this resolution are monomials whose exponents are parametrized by the coordinates of the corresponding point in $C_m$, and minimality of the resolution is achieved when the semigroup is maximal embedding dimension, which is the case parametrized by the interior of $C_m$ itself. |
| title | Minimal free resolutions of numerical semigroup algebras via Apéry specialization |
| topic | Commutative Algebra Combinatorics 20M14, 13D02, 52B05 (Primary), 05E40, 13F20, 13F65 (Secondary) |
| url | https://arxiv.org/abs/2310.03612 |