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Minimal free
resolutions of numerical semigroup algebras via Apéry
specialization
Benjamin Braun, Tara Gomes, Ezra Miller, Christopher O’Neill and Aleksandra Sobieska |
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Vol. 334 (2025), No. 2, 211–231
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Abstract |
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Numerical semigroups with multiplicity are parametrized by integer points in a polyhedral cone , 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 . The matrix entries of this resolution are monomials whose exponents are parametrized by the coordinates of the corresponding point in , and minimality of the resolution is achieved when the semigroup is of maximal embedding dimension, which is the case when it is parametrized by the interior of itself. |
Keywords
numerical semigroup, toric ideal, free resolution
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Mathematical Subject Classification
Primary: 13D02, 20M14, 52B05
Secondary: 05E40, 13F20, 13F65
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Milestones
Received: 19 June 2024
Revised: 3 January 2025
Accepted: 15 January 2025
Published: 8 February 2025
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Authors |
| Benjamin Braun | |
| Department of Mathematics University of Kentucky Lexington, KY United States |
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| Tara Gomes | |
| School of Mathematics University of Minnesota Minneapolis, MN United States |
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| Ezra Miller | |
| Department of Mathematics Duke University Durham, NC United States |
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| Christopher O’Neill | |
| Department of Mathematics and
Statistics San Diego State University San Diego, CA United States |
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| Aleksandra Sobieska | |
| Department of Mathematics Marshall University Huntington, WV United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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