Extensions of regular mappings and the Łojasiewicz exponent at infinity (Q630625)

Let \(F:V\to {\mathbb C}^m\) be a regular mapping, where \(V\subset {\mathbb C}^n\) is an algebraic set of positive dimension and \(m\geq n\geq 2\), and let \({\mathcal L}_\infty(F)\) be the Łojasiewicz exponent at infinity of \(F\). The main result of the paper is the existence of a polynomial extension \(G:{\mathbb C}^n\to {\mathbb C}^m\) of \(F\) with \({\mathcal L}_\infty (G)={\mathcal L}_\infty(F)\). Moreover, some estimates of the degree of \(G\) are given.