On a singular variety associated to a polynomial mapping

TL;DR

This paper generalizes a method linking the geometry of polynomial mappings' singularities at infinity to associated varieties' homology, extending previous results for broader classes of mappings.

Contribution

It extends the association between polynomial mappings and varieties to a more general setting, enhancing understanding of singularities at infinity.

Findings

Generalized the construction of associated varieties for polynomial mappings

Connected homology of these varieties to singularities at infinity

Broadened applicability of intersection homology in polynomial mapping analysis

Abstract

In the paper "Geometry of polynomial mapping at infinity via intersection homology" the second and third authors associated to a given polynomial mapping $F : \C^2 \to \C^2$ with nonvanishing jacobian a variety whose homology or intersection homology describes the geometry of singularities at infinity of the mapping. We generalize this result.