On the perturbations of Noetherian local domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915039559024640 |
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| author | Nguyen, Hong Duc Nguyen, Hop D. Quy, Pham Hung |
| author_facet | Nguyen, Hong Duc Nguyen, Hop D. Quy, Pham Hung |
| contents | We study how the properties of being reduced, integral domain, and normal, behave under small perturbations of the defining equations of a noetherian local ring. It is not hard to show that the property of being a local integral domain (reduced, normal ring) is not stable under small perturbations in general. We prove that perturbation stability holds in the following situations: (1) perturbation of being an integral domain for factorial excellent Henselian local rings; (2) perturbation of normality for excellent local complete intersections containing a field of characteristic zero; and (3) perturbation of reducedness for excellent local complete intersections containing a field of characteristic zero, and for factorial Nagata local rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the perturbations of Noetherian local domains Nguyen, Hong Duc Nguyen, Hop D. Quy, Pham Hung Commutative Algebra Algebraic Geometry 13D10, 13B40, 14B12 We study how the properties of being reduced, integral domain, and normal, behave under small perturbations of the defining equations of a noetherian local ring. It is not hard to show that the property of being a local integral domain (reduced, normal ring) is not stable under small perturbations in general. We prove that perturbation stability holds in the following situations: (1) perturbation of being an integral domain for factorial excellent Henselian local rings; (2) perturbation of normality for excellent local complete intersections containing a field of characteristic zero; and (3) perturbation of reducedness for excellent local complete intersections containing a field of characteristic zero, and for factorial Nagata local rings. |
| title | On the perturbations of Noetherian local domains |
| topic | Commutative Algebra Algebraic Geometry 13D10, 13B40, 14B12 |
| url | https://arxiv.org/abs/2411.19011 |