Fold singularities of the maps associated with Milnor fibration for mixed polynomials

Abstract

Milnor fibrations were extended by Mutsuo Oka for certain mixed polynomial. In this paper, we study singular points of differentiable maps into the 2-dimensional torus, called Milnor fibration product maps, obtained by several Milnor fibrations for mixed polynomial. We give a characterization of singular points of such product maps, and for the case of certain polar weighted homogeneous polynomials, a criterion for a fold singular point.

8 pages, Milnor fibration, singularity, fold, mixed polynomial, polar weighted homogeneous