Complete intersection vanishing ideals on degenerate tori over finite fields
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2012
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| _version_ | 1866911771491565568 |
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| author | Lopez, Hiram H. Villarreal, Rafael H. Zarate, Leticia |
| author_facet | Lopez, Hiram H. Villarreal, Rafael H. Zarate, Leticia |
| contents | We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a correspondence between vanishing ideals and toric ideals associated to numerical semigroups. This correspondence is shown to preserve the complete intersection property, and allows us to use some available algorithms to determine whether a given vanishing ideal is a complete intersection. We give formulae for the degree, and for the index of regularity of a complete intersection in terms of the Frobenius number and the generators of a numerical semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1207_0244 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Complete intersection vanishing ideals on degenerate tori over finite fields Lopez, Hiram H. Villarreal, Rafael H. Zarate, Leticia Commutative Algebra Algebraic Geometry Combinatorics 13F20, 14H45 We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a correspondence between vanishing ideals and toric ideals associated to numerical semigroups. This correspondence is shown to preserve the complete intersection property, and allows us to use some available algorithms to determine whether a given vanishing ideal is a complete intersection. We give formulae for the degree, and for the index of regularity of a complete intersection in terms of the Frobenius number and the generators of a numerical semigroup. |
| title | Complete intersection vanishing ideals on degenerate tori over finite fields |
| topic | Commutative Algebra Algebraic Geometry Combinatorics 13F20, 14H45 |
| url | https://arxiv.org/abs/1207.0244 |