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arXiv · 2411.19011

On the perturbations of Noetherian local domains

Hong Duc Nguyen·Hop D. Nguyen·Pham Hung Quy
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Abstract

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.

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Hong Duc Nguyen, Hop D. Nguyen, Pham Hung Quy. 2024-11-28. On the perturbations of Noetherian local domains. https://arxiv.org/abs/2411.19011

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