The Rational Hull of Rudin's Klein Bottle

2018/08/22 by Anderson, John T., Gupta, Purvi, Stout, Edgar L.
#32E20 #32V40 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.07310

Abstract

In this note, a general result for determining the rational hulls of fibered sets in ℂ² 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 ℂ². 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 ℂ².

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