English

On the Milnor fibration for $f(\mathbf z)\bar g(\mathbf z)$

Algebraic Geometry 2019-09-04 v3

Abstract

We consider a mixed function of type H(z,zˉ)=f(z)gˉ(z)H(\mathbf z,\bar {\mathbf z})=f(\mathbf z)\bar g(\mathbf z) where ff and gg are convenient holomorphic functions which have isolated critical points at the origin and we assume that the intersection f=g=0f=g=0 is a complete intersection variety with an isolated singlarity at theorigin. We assume also that HH satisfies the multiplicity condition.We will show that HH has a tubular Milnor fibration and also a spherical Milnor fibration. We give examples which does not satisfy the Newton multiplicity condition where one does not have Milnor fibration and the others have Milnor fibrations.

Keywords

Cite

@article{arxiv.1812.10909,
  title  = {On the Milnor fibration for $f(\mathbf z)\bar g(\mathbf z)$},
  author = {Mutsuo Oka},
  journal= {arXiv preprint arXiv:1812.10909},
  year   = {2019}
}