Computing efficiently the non-properness set of polynomial maps on the plane

Boulos El Hilany, Elias Tsigaridas

Published 2021-01-13Version 1

We present mathematical, algorithmic, complexity, and implementation results on the problem of computing the Jelonek set in 2D. This is the set in $\mathbb{K}^2$ at which a polynomial map $f: \mathbb{K}^2 \to \mathbb{K}^2$ is not proper. Our results make no assumptions on $f$ and are valid for $\mathbb{K}= \mathbb{C}$ and $\mathbb{K} = \mathbb{R}$.