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 $\mathbb {C}^2$.References
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Additional Information
- John T. Anderson
- Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610
- MR Author ID: 251416
- Email: janderso@holycross.edu
- Purvi Gupta
- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
- MR Author ID: 960836
- Email: purvi.gupta@rutgers.edu
- Edgar L. Stout
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- MR Author ID: 167815
- Email: stout@math.washington.edu
- Received by editor(s): August 20, 2018
- Received by editor(s) in revised form: December 4, 2018, and December 17, 2018
- Published electronically: April 18, 2019
- Communicated by: Harold P. Boas
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3859-3866
- MSC (2010): Primary 32E20; Secondary 32V40
- DOI: https://doi.org/10.1090/proc/14514
- MathSciNet review: 3993778