余秩为2余维为7的光滑函数芽的分类

郭瑞芝

DOI：10.7612/j.issn.10002537.2017.02.011

摘要本文利用有限決定性理论、分裂引理和Nakayama引理，建立光滑函数芽Jacobi理想的下降序列，考虑Jacobi理想的余维分布，得到了右等价下余秩为2余维为7的光滑函数芽的完整分类，并且给出了这类函数芽的标准形.

关键词右等价；余维；余秩；分类

中图分类号O192文献标识码A文章编号10002537（2017）02006610

Classification of Germs of Smooth Functions with Corank 2 and Codimension 7

GUO Ruizhi*， SHI Gaoli

（College of Mathematics and Computer Science， Hunan Normal University， Changsha 410081， China）

AbstractBy using of the theory of finite determinacy， splitting lemma and Nakayama lemma， in this paper， we have established a decreasing sequence with Jacobi ideal of a germ of smooth functions. We have also examined the distribution of codimension of the Jacobi ideal. The classification of germs of smooth functions with corank 2 and codimension 7 under the condition of right equivalence has been obtained， with normal forms of this germs explicitly given.

Key wordsright equivalence； codimension； corank； classification