The University of Sydney - School of Mathematics and Statistics

Topology of polynomial mapping from ${\mathbb{C}}^n$ to ${\mathbb{C}}^{n-1}$ (joint w.w. Ha Huy Vui)

Nguyen Tat Thang Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi

Abstract

Let F: ${\mathbb{C}}^n$ to ${\mathbb{C}}^m$ be a polynomial mapping. It is well-known that F is a locally trivial fibration outside some subset of ${\mathbb{C}}^m$, the smallest such set is called the bifurcation set of the map, denoted by B(F). It is a natural question that how to determine the set B(F). We know the answer for only few cases, namely polynomial functions in two variables or functions having only isolated singularities at infinity. In this talk, we give a description for bifurcation set of polynomial mappings from ${\mathbb{C}}^n$ to ${\mathbb{C}}^{n-1}$ which satisfy an additional assumption.