Classification of ℤ3-Equivariant Simple Function Germs

Abstract

The present paper deals with the classification of multivariate holomorphic function germs that are equivariant simple under representations of cyclic groups. We obtain a complete classification of such function germs of two and three variables for all possible nontrivial ℤ₃-actions. Our main classification methods generalize those used for the classification of simple germs in the nonequivariant case.