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Holomorphic families of long $ \mathbb{C}^2$'s


Author: Franc Forstnerič
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
Published electronically: November 3, 2011
MathSciNet review: 2898700
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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$.


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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
Email: franc.forstneric@fmf.uni-lj.si

DOI: https://doi.org/10.1090/S0002-9939-2011-11092-X
Keywords: Stein manifold, Fatou-Bieberbach domain, long $\mathbb{C}^{2}$
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
Article copyright: © Copyright 2011 American Mathematical Society

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