The Rational Hull of Rudin's Klein Bottle
John T. Anderson, Purvi Gupta, Edgar L. Stout

TL;DR
This paper develops a method to compute the rational hulls of fibered sets in complex two-space and applies it to explicitly determine the rational hull of Rudin's Klein bottle, a nonorientable surface.
Contribution
It introduces a general approach for calculating rational hulls of fibered sets and provides the first explicit computation of the rational hull of Rudin's Klein bottle.
Findings
Rudin's Klein bottle has a two-dimensional rational hull.
The rational hull differs from the polynomial hull, which contains an open set.
The method applies to other surfaces in a72.
Abstract
In this note, a general result for determining the rational hulls of fibered sets in 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 . 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 .
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