On Rees algebras of 2-determinantal ideals
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929373692559360 |
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| author | Ramkumar, Ritvik Sammartano, Alessio |
| author_facet | Ramkumar, Ritvik Sammartano, Alessio |
| contents | Let I be the ideal of minors of a 2 by n matrix of linear forms with the expected codimension. In this paper we prove that the Rees algebra of I and its special fiber ring are Cohen-Macaulay and Koszul; in particular, they are quadratic algebras. The main novelty in our approach is the analysis of a stratification of the Hilbert scheme of determinantal ideals. We study degenerations of Rees algebras along this stratification, and combine it with certain squarefree Groebner degenerations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12668 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Rees algebras of 2-determinantal ideals Ramkumar, Ritvik Sammartano, Alessio Commutative Algebra Algebraic Geometry 13A30, 13C40, 05E40, 13D10, 13F55, 13H10, 13P10, 14C05 Let I be the ideal of minors of a 2 by n matrix of linear forms with the expected codimension. In this paper we prove that the Rees algebra of I and its special fiber ring are Cohen-Macaulay and Koszul; in particular, they are quadratic algebras. The main novelty in our approach is the analysis of a stratification of the Hilbert scheme of determinantal ideals. We study degenerations of Rees algebras along this stratification, and combine it with certain squarefree Groebner degenerations. |
| title | On Rees algebras of 2-determinantal ideals |
| topic | Commutative Algebra Algebraic Geometry 13A30, 13C40, 05E40, 13D10, 13F55, 13H10, 13P10, 14C05 |
| url | https://arxiv.org/abs/2210.12668 |