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Automorphisms of affine smooth varieties


Authors: Zbigniew Jelonek and Tomasz Lenarcik
Journal: Proc. Amer. Math. Soc. 142 (2014), 1157-1163
MSC (2010): Primary 13C10, 14J70, 14R99
Published electronically: January 30, 2014
MathSciNet review: 3162238
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Abstract: Let $ k$ be an algebraically closed field. If $ X$ is a smooth projective variety over $ k$ and $ H\subset X$ is a very ample hypersurface without ruled components, then the group $ \mathrm {Aut}(X\setminus H)$ is finite and equal to $ \mathrm {Stab}_X(H)=\{ \phi \in \mathrm {Aut}(X): \phi (H)=H\}.$


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Additional Information

Zbigniew Jelonek
Affiliation: Instytut Matematyczny PAN, ul. Śniadeckich 8, 00-956 Warszawa, Poland
Email: najelone@cyf-kr.edu.pl

Tomasz Lenarcik
Affiliation: Faculty of Mathematics and Computer Science, Jagiellonian Univeristy, ul. prof. Stanisława Łojasiewicza 6, 30-348 Kraków, Poland
Email: Tomasz.Lenarcik@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12033-8
Keywords: Algebraic automorphism, complete intersection, affine variety
Received by editor(s): November 2, 2011
Received by editor(s) in revised form: May 11, 2012
Published electronically: January 30, 2014
Additional Notes: The first author acknowledges support of the Polish Ministry of Science and Higher Education, grant MNiSW N N201 420939, 2010–2013.
Communicated by: Harm Derksen
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.