A Fatou-Bieberbach domain avoiding a neighborhood of a variety of codimension 2 (Q1568699)

The authors prove the following Theorem. Let \(V\) be an algebraic variety of codimension 2 in \(\mathbb{C}^n\). Then there exists a neighborhood \(U\) of \(V\) and an injective holomorphic map \(\Phi:\mathbb{C}^n \to\mathbb{C}^n \setminus U\). This answers a question of Y.-T. Siu showing that there is a Fatou-Bieberbach domain (i.e., a proper subdomain in \(\mathbb{C}^n\) biholomorphic to \(\mathbb{C}^n)\) in the complement of some neighborhood of an algebraic subvariety of codimension two.