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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Rational surfaces with a large group of automorphisms
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by Serge Cantat and Igor Dolgachev PDF
J. Amer. Math. Soc. 25 (2012), 863-905


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
  • MR Author ID: 614455
  • Email:
  • Igor Dolgachev
  • Affiliation: Department of Mathematics, University of Michigan, 525 E. University Avenue, Ann Arbor, Michigan, 49109
  • MR Author ID: 58860
  • Email:
  • 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
  • © Copyright 2012 by the authors
  • Journal: J. Amer. Math. Soc. 25 (2012), 863-905
  • MSC (2010): Primary 14E07, 14J26, 14J50, 20F55, 32H50
  • DOI:
  • MathSciNet review: 2904576