Classification Of Germs Of Smooth Functions With Corank 2

By the theory of finite determinacy,splitting lemma and Nakayama lemma,we establishe a decreasing sequence with Jacobi ideal of a germ of smooth func-tion,and consider the distribution of codimension of the Jacobi ideal,then we discusse the classification of germs of smooth functions with corank 2 under conditions of right equivalence.It consists of three chapters.In the first chapter,we introduce the development of singularity t.heory background and the research dynamic of germs of smooth functions classifica-tion.In the second chapter,we introduce some basic mathematical symbols,several important lemma(splitting lemma and Nakayama lemma)and related thesis and conclusions.In the third chapter,firstly we give the complete classification of germs of smooth functions with corank 2 and codimension 7 and we get the related normal forms,secondly we give the complete classification of germs of smooth functions with corank 2 and codimension 8,finally we generalize to the condi-tions with corank 2 and codimension 2k(k ? 3),and obtains the corresponding normal forms.