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arXiv · 1808.07310

The Rational Hull of Rudin's Klein Bottle

John T. Anderson·Purvi Gupta·Edgar L. Stout
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Abstract

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 $\mathbb{C}^2$.

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John T. Anderson, Purvi Gupta, Edgar L. Stout. 2018-08-22. The Rational Hull of Rudin's Klein Bottle. https://arxiv.org/abs/1808.07310

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