Homogeneous Border Bases on Infinite Order Ideals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917318216384512 |
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| author | Bertone, Cristina Bovero, Sofia |
| author_facet | Bertone, Cristina Bovero, Sofia |
| contents | Border bases are traditionally restricted to 0-dimensional ideals due to the finiteness of the underlying order ideal. In this paper we extend the theory to homogeneous ideals of positive Krull dimension by introducing homogeneous border bases, defined relative to an infinite order ideal. Moreover, we provide two characterizations of these bases: one via border reductors and, most notably, one in terms of formal multiplication matrices. Although the latter condition a priori requires verification in infinitely many degrees, we prove that it is sufficient to check only finitely many of them, thereby obtaining an effective criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06155 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homogeneous Border Bases on Infinite Order Ideals Bertone, Cristina Bovero, Sofia Commutative Algebra 13P10, 14Q20 Border bases are traditionally restricted to 0-dimensional ideals due to the finiteness of the underlying order ideal. In this paper we extend the theory to homogeneous ideals of positive Krull dimension by introducing homogeneous border bases, defined relative to an infinite order ideal. Moreover, we provide two characterizations of these bases: one via border reductors and, most notably, one in terms of formal multiplication matrices. Although the latter condition a priori requires verification in infinitely many degrees, we prove that it is sufficient to check only finitely many of them, thereby obtaining an effective criterion. |
| title | Homogeneous Border Bases on Infinite Order Ideals |
| topic | Commutative Algebra 13P10, 14Q20 |
| url | https://arxiv.org/abs/2603.06155 |