On a singular variety associated to a polynomial mapping from $\C^n$ to $\C^{n-1}$

Abstract

We construct a singular variety ${\mathcal{V}}_G$ associated to a polynomial mapping $G : \C^{n} \to \C^{n - 1}$ where $n\ge 2$. We prove that in the case $G : \C^{3} \to \C^{2}$, if $G$ is a local submersion but is not a fibration, then the homology and the intersection homology with total perversity (with compact supports or closed supports) in dimension two of the variety ${\mathcal{V}}_G$ is not trivial. In the case of a local submersion $G : \C^{n} \to \C^{n - 1}$ where $n\ge 4$, the result is still true with an additional condition.

References in corpus (3)

• Regularity at infinity of real mappings and a Morse-Sard theorem
• On a singular variety associated to a polynomial mapping
• Geometry of polynomial mappings at infinity via intersection homology

Cited by in corpus (1)

• Some classes satisfying the 2-dimensional Jacobian conjecture and a proof of the complex conjecture until degree 104