On the perturbations of Noetherian local domains
| Autor: | Nguyen, Hong Duc, Nguyen, Hop D., Quy, Pham Hung |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 15 pages, comments are very well-come |
| Databáze: | arXiv |
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