一般约化曲线族中的 Whitney 等奇异性
复变函数
2019-04-15 v2
摘要
本文研究单参数平坦一般约化曲线族中的等奇异性。我们考虑若干等奇异性判据：拓扑平凡性、Whitney 等奇异性与强同时消解。在此背景下，我们证明 Whitney 等奇异性等价于强同时消解，也等价于纤维的 Milnor 数与重数的常值性。这些结果将已知约化曲线上的结果推广到一般约化曲线的平坦形变情形。当族 拓扑平凡时，我们还通过与该族参数空间相关的某一局部环的 Cohen-Macaulay 性质来刻画 Whitney 等奇异性。
引用
@article{arxiv.1809.03630,
title = {Whitney equisingularity in families of generically reduced curves},
author = {O. N. Silva and J. Snoussi},
journal= {arXiv preprint arXiv:1809.03630},
year = {2019}
}
备注
Changes: A new result showing the connectivity of the fibers under the hypothesis on the constancy of the multiplicity of the fibers has been added (Lemma 4.6). Hence, the hypothesis about the connectivity of the fibers $X_t$ in Theorem 3.3 (first version) was omitted. Typos have been corrected, precise or missing references have been added. Some points that were not clear were better explained