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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2601.02612 |
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| _version_ | 1866917186223734784 |
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| author | Chlopecki, Anna Natalie Gallup, Nathaniel Meintjes, Jason |
| author_facet | Chlopecki, Anna Natalie Gallup, Nathaniel Meintjes, Jason |
| contents | We show that, under certain constraints, the Stanley-Reisner ring of an infinite simplicial complex is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. We apply this result to prove the wanted claim -- that initial complexes of matrix Schubert varieties corresponding to infinite permutations in $S_{\infty}$ with respect to an antidiagonal term order are Cohen-Macaulay (in the same sense), giving rise to new examples of non-Noetherian Cohen-Macaulay rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02612 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Antidiagonal Initial Complexes of Infinite Matrix Schubert Varieties are Cohen-Macaulay Chlopecki, Anna Natalie Gallup, Nathaniel Meintjes, Jason Commutative Algebra Combinatorics 13C14, 13C70, 13C11 We show that, under certain constraints, the Stanley-Reisner ring of an infinite simplicial complex is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. We apply this result to prove the wanted claim -- that initial complexes of matrix Schubert varieties corresponding to infinite permutations in $S_{\infty}$ with respect to an antidiagonal term order are Cohen-Macaulay (in the same sense), giving rise to new examples of non-Noetherian Cohen-Macaulay rings. |
| title | Antidiagonal Initial Complexes of Infinite Matrix Schubert Varieties are Cohen-Macaulay |
| topic | Commutative Algebra Combinatorics 13C14, 13C70, 13C11 |
| url | https://arxiv.org/abs/2601.02612 |