ИСТИНА

The concept of an equivariant map naturally arises in the study of manifolds with actions of a fixed group: equivariant maps are maps that commute with group actions on the source and target. The group of equivariant automorphisms of a manifold acts on the space of equivariant maps of this manifold. The structure of orbits of this action is often complicated: it can include discrete (finite or countable) families of orbits as well as continuous ones. An orbit is called equivariant simple if its sufficiently small neighborhood intersects only a finite number of other orbits. The talk is devoted to the study of singular multivariate holomorphic function germs that are equivariant simple with respect to a pair of actions of a finite cyclic group on the source and target. In particular, a complete classification of such germs in two and three variables will be presented for the group of three elements.