Existence of minimal models for varieties of log general type

Birkar, Caucher; Cascini, Paolo; Hacon, Christopher; McKernan, James

doi:10.1090/S0894-0347-09-00649-3

Existence of minimal models for varieties of log general type

Authors: Caucher Birkar, Paolo Cascini, Christopher D. Hacon and James M^cKernan
Journal: J. Amer. Math. Soc. 23 (2010), 405-468
MSC (2010): Primary 14E30
DOI: https://doi.org/10.1090/S0894-0347-09-00649-3
Published electronically: November 13, 2009
MathSciNet review: 2601039
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the canonical ring of a smooth projective variety is finitely generated.

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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
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
Email: hacon@math.utah.edu

James M^cKernan
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

DOI: https://doi.org/10.1090/S0894-0347-09-00649-3
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.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.