Buchsbaumness, Macaulayfication and Castelnuovo-Mumford regularity of monomial curves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909659991900160 |
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| author | Dawn, Biplab Saloni, Kumari |
| author_facet | Dawn, Biplab Saloni, Kumari |
| contents | Projective monomial curves are associated with rings generated by monomials of equal degree in two variables. In this paper, we give an infinite class of non-smooth, non Cohen-Macaulay $k$-Buchsbaum projective monomial curves for any $k\geq 1$ and find the monomial generators for the respective Macaulayfication. More generally, we demonstrate a method to find the Macaulayfication of a $k$-Buchsbaum monomial curve for any $k\geq 1$. We also discuss Castelnuovo-Mumford regularity of certain curves in terms of $k$-Buchsbaumness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Buchsbaumness, Macaulayfication and Castelnuovo-Mumford regularity of monomial curves Dawn, Biplab Saloni, Kumari Commutative Algebra 13F65, 14H20, 13D45, 13H10, 14B15 Projective monomial curves are associated with rings generated by monomials of equal degree in two variables. In this paper, we give an infinite class of non-smooth, non Cohen-Macaulay $k$-Buchsbaum projective monomial curves for any $k\geq 1$ and find the monomial generators for the respective Macaulayfication. More generally, we demonstrate a method to find the Macaulayfication of a $k$-Buchsbaum monomial curve for any $k\geq 1$. We also discuss Castelnuovo-Mumford regularity of certain curves in terms of $k$-Buchsbaumness. |
| title | Buchsbaumness, Macaulayfication and Castelnuovo-Mumford regularity of monomial curves |
| topic | Commutative Algebra 13F65, 14H20, 13D45, 13H10, 14B15 |
| url | https://arxiv.org/abs/2506.20473 |