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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

   

 

Rational surfaces with a large group of automorphisms


Authors: Serge Cantat and Igor Dolgachev
Journal: J. Amer. Math. Soc. 25 (2012), 863-905
MSC (2010): Primary 14E07, 14J26, 14J50, 20F55, 32H50
Published electronically: February 23, 2012
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Abstract: We classify rational surfaces $ X$ for which the image of the automorphism group $ \mathrm {Aut}(X)$ in the group of linear transformations of the Picard group $ \mathrm {Pic}(X)$ is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in terms of periodic orbits of birational actions of infinite Coxeter groups.


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Additional Information

Serge Cantat
Affiliation: IRMAR, UMR 6625 du CNRS et Université de Rennes 1, Bât. 22-23 du Campus de Beaulieu, F-35042 Rennes cedex; DMA, UMR 8553 du CNRS, École Normale Supérieure de Paris, 45 rue d’Ulm, F-75230 Paris cedex 05
Email: serge.cantat@univ-rennes1.fr

Igor Dolgachev
Affiliation: Department of Mathematics, University of Michigan, 525 E. University Avenue, Ann Arbor, Michigan, 49109
Email: idolga@umich.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00732-2
PII: S 0894-0347(2012)00732-2
Received by editor(s): July 5, 2011
Received by editor(s) in revised form: December 9, 2011, and January 23, 2012
Published electronically: February 23, 2012
Article copyright: © Copyright 2012 by the authors