Generalized mixed product ideals whose powers have a linear resolution
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910392325767168 |
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| author | La Barbiera, Monica Moghimipor, Roya |
| author_facet | La Barbiera, Monica Moghimipor, Roya |
| contents | In this paper we study classes of monomial ideals for which all of its powers have a linear resolution. Let K[x_{1},x_{2}] be the polynomial ring in two variables over the field K, and let L be the generalized mixed product ideal induced by a monomial ideal I. It is shown that, if I\subset K[x_1,x_2] and the ideals substituting the monomials in I are Veronese type ideals, then L^{k} has a linear resolution for all k\geq 1. Furthermore, we compute some algebraic invariants of generalized mixed product ideals induced by a transversal polymatroidal ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized mixed product ideals whose powers have a linear resolution La Barbiera, Monica Moghimipor, Roya Commutative Algebra 13C13, 13D02 In this paper we study classes of monomial ideals for which all of its powers have a linear resolution. Let K[x_{1},x_{2}] be the polynomial ring in two variables over the field K, and let L be the generalized mixed product ideal induced by a monomial ideal I. It is shown that, if I\subset K[x_1,x_2] and the ideals substituting the monomials in I are Veronese type ideals, then L^{k} has a linear resolution for all k\geq 1. Furthermore, we compute some algebraic invariants of generalized mixed product ideals induced by a transversal polymatroidal ideal. |
| title | Generalized mixed product ideals whose powers have a linear resolution |
| topic | Commutative Algebra 13C13, 13D02 |
| url | https://arxiv.org/abs/2404.00080 |