On the Milnor fibration for $f(\boldsymbol{z}) \bar{g}(\boldsymbol{z})$ II

Abstract

We consider a mixed function of type $H(\boldsymbol{z}, \bar{\boldsymbol{z}}) = f(\boldsymbol{z}) \bar{g} (\boldsymbol{z})$ where $f$ and $g$ are holomorphic functions which are non-degenerate with respect to the Newton boundaries. We assume also that the variety $f = g = 0$ is a non-degenerate complete intersection variety. In our previous paper, we considered the case that $f, g$ are convenient so that they have isolated singularities. In this paper we do not assume the convenience of $f$ and $g$. In non-convenient case, two hypersurfaces may have non-isolated singularities at the origin. We will show that $H$ still has both a tubular and a spherical Milnor fibrations under the local tame non-degeneracy and the toric multiplicity condition. We also prove the equivalence of two fibrations.