The v-numbers of Stanley-Reisner ideals from the viewpoint of Alexander dual complexes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911089634050048 |
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| author | Kataoka, Tatsuya Muta, Yuji Terai, Naoki |
| author_facet | Kataoka, Tatsuya Muta, Yuji Terai, Naoki |
| contents | We express the v-number of the Stanley-Reisner ideal in terms of its Alexander dual complex and prove that the v-number of a cover ideal is just two less than the initial degree of the its syzygy module. We give some relation between the v-number of the Stanley-Reisner ideal and the Serre-depth of the quotient ring of the second symbolic power of the Stanley-Reisner ideal of its Alexander dual. We also show that the v-number of the Stanley-Reisner ideal of a 2-pure simplicial complex is equal to the dimension of its Stanley-Reisner ring. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_07535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The v-numbers of Stanley-Reisner ideals from the viewpoint of Alexander dual complexes Kataoka, Tatsuya Muta, Yuji Terai, Naoki Commutative Algebra We express the v-number of the Stanley-Reisner ideal in terms of its Alexander dual complex and prove that the v-number of a cover ideal is just two less than the initial degree of the its syzygy module. We give some relation between the v-number of the Stanley-Reisner ideal and the Serre-depth of the quotient ring of the second symbolic power of the Stanley-Reisner ideal of its Alexander dual. We also show that the v-number of the Stanley-Reisner ideal of a 2-pure simplicial complex is equal to the dimension of its Stanley-Reisner ring. |
| title | The v-numbers of Stanley-Reisner ideals from the viewpoint of Alexander dual complexes |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2504.07535 |