On the perturbations of Noetherian local domains
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.
Keywords
Cite
@article{arxiv.2411.19011,
title = {On the perturbations of Noetherian local domains},
author = {Hong Duc Nguyen and Hop D. Nguyen and Pham Hung Quy},
journal= {arXiv preprint arXiv:2411.19011},
year = {2024}
}
Comments
15 pages, comments are very well-come