The Rational Hull of Rudin's Klein Bottle

In this note, a general result for determining the rational hulls of fibered sets in ${\mathbb{C}}^2$ 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 ${\mathbb{C}}^2$. 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 two-dimensional. Using the same method, we also compute the rational hulls of some other surfaces in ${\mathbb{C}}^2$.