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Analytic extensions of algebraic isomorphisms


Author: S. Kaliman
Journal: Proc. Amer. Math. Soc. 143 (2015), 4571-4581
MSC (2010): Primary 14R20, 32M17
DOI: https://doi.org/10.1090/proc/12684
Published electronically: June 10, 2015
MathSciNet review: 3391018
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Abstract: Let $ \Psi : X_1 \to X_2$ be an isomorphism of closed affine algebraic subvarieties of $ \mathbb{C}^n$ such that $ n > \max (2\dim X_1, \dim TX_1)$. We prove that $ \Psi $ can be extended to a holomorphic automorphism of $ \mathbb{C}^n$. Furthermore, when $ \Psi $ is an isomorphism of curves, such an extension exists for every $ n\geq 3$ even when $ \dim \,TX_1=n$.


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Additional Information

S. Kaliman
Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
Email: kaliman@math.miami.edu

DOI: https://doi.org/10.1090/proc/12684
Keywords: Affine varieties, group actions, one-parameter subgroups, transitivity
Received by editor(s): September 15, 2013
Received by editor(s) in revised form: October 26, 2013
Published electronically: June 10, 2015
Additional Notes: This research was partially done during a visit of the author to the Max-Planck-Institute of Mathematics, Bonn. He thanks this institution for generous support and excellent working conditions.
Communicated by: Harm Derksen
Article copyright: © Copyright 2015 American Mathematical Society