Holomorphic families of long $\mathbb {C}^2$’s
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Abstract:
We construct a holomorphically varying family of complex surfaces $X_s$, parametrized by the points $s$ in any Stein manifold, such that every $X_s$ is a long $\mathbb {C}^2$ which is biholomorphic to $\mathbb {C}^2$ for some but not all values of $s$.References
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Additional Information
- Franc Forstnerič
- Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
- MR Author ID: 228404
- Email: franc.forstneric@fmf.uni-lj.si
- Received by editor(s): January 18, 2011
- Received by editor(s) in revised form: February 17, 2011
- Published electronically: November 3, 2011
- Additional Notes: The author was supported by grants P1-0291 and J1-2152 from ARRS, Republic of Slovenia
- Communicated by: Mei-Chi Shaw
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 2383-2389
- MSC (2010): Primary 32E10, 32E30, 32H02
- DOI: https://doi.org/10.1090/S0002-9939-2011-11092-X
- MathSciNet review: 2898700