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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Automorphisms of $ \mathbb{A}^{1}$-fibered affine surfaces


Authors: Jérémy Blanc and Adrien Dubouloz
Journal: Trans. Amer. Math. Soc. 363 (2011), 5887-5924
MSC (2010): Primary 14R25, 14R20, 14R05, 14E05
Published electronically: June 1, 2011
MathSciNet review: 2817414
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Abstract: We develop techniques of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface $ S$ of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of $ S$ is generated by automorphisms preserving these fibrations.


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Additional Information

Jérémy Blanc
Affiliation: Section de mathématiques, Université de Genève, 2-4 rue du Lièvre Case postale 64, 1211 Genève 4, Suisse
Address at time of publication: Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Suisse
Email: Jeremy.Blanc@unige.ch, Jeremy.Blanc@unibas.ch

Adrien Dubouloz
Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary - BP 47870, 21078 Dijon cedex, France
Email: Adrien.Dubouloz@u-bourgogne.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05266-9
PII: S 0002-9947(2011)05266-9
Received by editor(s): July 4, 2009
Received by editor(s) in revised form: November 29, 2009
Published electronically: June 1, 2011
Additional Notes: This research has been partially supported by FABER Grant 07-512-AA-010-S-179
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.