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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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Existence of minimal models for varieties of log general type
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by Caucher Birkar, Paolo Cascini, Christopher D. Hacon and James McKernan HTML | PDF
J. Amer. Math. Soc. 23 (2010), 405-468 Request permission

Abstract:

We prove that the canonical ring of a smooth projective variety is finitely generated.
References
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Additional Information
  • Caucher Birkar
  • Affiliation: DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
  • Email: c.birkar@dpmms.cam.ac.uk
  • Paolo Cascini
  • Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106 and Imperial College London, 180 Queens Gate, London SW7 2A2, United Kingdom
  • MR Author ID: 674262
  • Email: cascini@math.ucsb.edu, p.cascini@imperial.ac.uk
  • Christopher D. Hacon
  • Affiliation: Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, Utah 84112
  • MR Author ID: 613883
  • Email: hacon@math.utah.edu
  • James McKernan
  • Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106 and Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • Email: mckernan@math.ucsb.edu, mckernan@math.mit.edu
  • Received by editor(s): August 13, 2008
  • Published electronically: November 13, 2009
  • Additional Notes: The first author was partially supported by EPSRC grant GR/S92854/02
    The second author was partially supported by NSF research grant no: 0801258
    The third author was partially supported by NSF research grant no: 0456363 and an AMS Centennial fellowship
    The fourth author was partially supported by NSA grant no: H98230-06-1-0059 and NSF grant no: 0701101 and would like to thank Sogang University and Professor Yongnam Lee for their generous hospitality, where some of the work for this paper was completed
    All authors would like to thank Dan Abramovich, Valery Alexeev, Florin Ambro, Tommaso de Fernex, Stephane Dreul, Seán Keel, Kalle Karu, János Kollár, Sándor Kovács, Michael McQuillan, Shigefumi Mori, Martin Olsson, Genia Tevelev, Burt Totaro, Angelo Vistoli and Chengyang Xu for answering many of our questions and pointing out some errors in an earlier version of this paper. They would also like to thank the referee for some useful comments.
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 23 (2010), 405-468
  • MSC (2010): Primary 14E30
  • DOI: https://doi.org/10.1090/S0894-0347-09-00649-3
  • MathSciNet review: 2601039