Castelnuovo-Mumford regularity of unprojections and the Eisenbud-Goto regularity conjecture
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909289193406464 |
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| author | Choe, Junho |
| author_facet | Choe, Junho |
| contents | McCullough and Peeva found sequences of counterexamples to the Eisenbud--Goto conjecture on the Castelnuovo--Mumford regularity by using Rees-like algebras, where entries of each sequence have increasing dimensions and codimensions. In this paper we suggest another method to construct counterexamples to the conjecture with any fixed dimension $n\geq3$ and any fixed codimension $e\geq2$. Our strategy is an unprojection process and utilizes the possible complexity of homogeneous ideals with three generators. Furthermore, our counterexamples exhibit how singularities affect the Castelnuovo--Mumford regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_06151 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Castelnuovo-Mumford regularity of unprojections and the Eisenbud-Goto regularity conjecture Choe, Junho Algebraic Geometry Commutative Algebra 14N05 (Primary) 13D02 (Secondary) McCullough and Peeva found sequences of counterexamples to the Eisenbud--Goto conjecture on the Castelnuovo--Mumford regularity by using Rees-like algebras, where entries of each sequence have increasing dimensions and codimensions. In this paper we suggest another method to construct counterexamples to the conjecture with any fixed dimension $n\geq3$ and any fixed codimension $e\geq2$. Our strategy is an unprojection process and utilizes the possible complexity of homogeneous ideals with three generators. Furthermore, our counterexamples exhibit how singularities affect the Castelnuovo--Mumford regularity. |
| title | Castelnuovo-Mumford regularity of unprojections and the Eisenbud-Goto regularity conjecture |
| topic | Algebraic Geometry Commutative Algebra 14N05 (Primary) 13D02 (Secondary) |
| url | https://arxiv.org/abs/2206.06151 |