The rational hull of Rudin’s Klein bottle

Abstract

In this note, a general result for determining the rational hulls of fibered sets in C 2 \mathbb {C}^2 is established. We use this to compute the rational hull of Rudin’s Klein bottle, the first explicit example of a totally real nonorientable surface in C 2 \mathbb {C}^2 . In contrast to its polynomial hull, which was shown to contain an open set by the first author in 2012, its rational hull is shown to be 2 2 -dimensional. Using the same method, we also compute the rational hulls of some other surfaces in C 2 \mathbb {C}^2 .