On the Milnor fibration for 𝑓(𝒛) 𝑔̅ (𝒛) II

Abstract

We consider a mixed function of type 𝐻(𝒛, 𝒛̅ ) = 𝑓(𝒛) 𝑔̅ (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.