余秩為2余維為7的光滑函數芽的分類

郭瑞芝

DOI：10.7612/j.issn.10002537.2017.02.011

摘要本文利用有限決定性理論、分裂引理和Nakayama引理，建立光滑函數芽Jacobi理想的下降序列，考慮Jacobi理想的余維分布，得到了右等價下余秩為2余維為7的光滑函數芽的完整分類，并且給出了這類函數芽的標準形.

關鍵詞右等價；余維；余秩；分類

中圖分類號O192文獻標識碼A文章編號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