Polynomially convex hulls of unions of real planes in \({\mathbb C}^ n\)
Building on the work of \textit{B. Weinstock} [Math. Ann. 282, No. 1, 131--138 (1988; Zbl 0628.32015)] about the union of two subspaces, we show that \({\mathbb C}^ n\) can be obtained as the polynomially convex hull of a finite union of maximal totally real vector subspaces for any n greater than one. This is in sharp contrast with the fact that it takes a set of positive capacity of complex lines in \({\mathbb C}^ 2\) to obtain the whole space as hull. The special case of three real planes of \({\mathbb C}^ 2\) is studied: if the three pairwise unions are not polygonally convex, the hull contains an open cone but is smaller than \({\mathbb C}^ 2\).
scientific article; zbMATH DE number 4127602