The rational hull of Rudin’s Klein bottle

Anderson, John; Gupta, Purvi; Stout, Edgar

doi:10.1090/proc/14514

The rational hull of Rudin’s Klein bottle
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by John T. Anderson, Purvi Gupta and Edgar L. Stout PDF

Proc. Amer. Math. Soc. 147 (2019), 3859-3866 Request permission

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 $2$-dimensional. Using the same method, we also compute the rational hulls of some other surfaces in $\mathbb {C}^2$.

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