The Sarkisov program
Authors:
Christopher D. Hacon and James McKernan
Journal:
J. Algebraic Geom. 22 (2013), 389-405
DOI:
https://doi.org/10.1090/S1056-3911-2012-00599-2
Published electronically:
December 12, 2012
MathSciNet review:
3019454
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Abstract |
References |
Additional Information
Abstract: Any two birational Mori fibre spaces are connected by a sequence of Sarkisov links.
References
- Victor V. Batyrev, The cone of effective divisors of threefolds, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989) Contemp. Math., vol. 131, Amer. Math. Soc., Providence, RI, 1992, pp. 337–352. MR 1175891
- Caucher Birkar, Paolo Cascini, Christopher D. Hacon, and James McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405–468. MR 2601039, DOI https://doi.org/10.1090/S0894-0347-09-00649-3
- Andrea Bruno and Kenji Matsuki, Log Sarkisov program, Internat. J. Math. 8 (1997), no. 4, 451–494. MR 1460896, DOI https://doi.org/10.1142/S0129167X97000238
- Alessio Corti, Factoring birational maps of threefolds after Sarkisov, J. Algebraic Geom. 4 (1995), no. 2, 223–254. MR 1311348
- Yi Hu and Sean Keel, Mori dream spaces and GIT, Michigan Math. J. 48 (2000), 331–348. Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786494, DOI https://doi.org/10.1307/mmj/1030132722
- Yujiro Kawamata, Flops connect minimal models, Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, 419–423. MR 2426353, DOI https://doi.org/10.2977/prims/1210167332
- V. V. Shokurov, $3$-fold log models, J. Math. Sci. 81 (1996), no. 3, 2667–2699. Algebraic geometry, 4. MR 1420223, DOI https://doi.org/10.1007/BF02362335
References
- V. Batyrev, The cone of effective divisors of threefolds, Proc. Intl. Conf. on Algebra, 1989, pp. 337–352. MR 1175891 (94f:14035)
- C. Birkar, P. Cascini, C. Hacon, and J. McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405–468. MR 2601039 (2011f:14023)
- A. Bruno and K. Matsuki, Log Sarkisov program, Internat. J. Math. 8 (1997), no. 4, 451–494. MR 1460896 (98h:14017)
- A. Corti, Factoring birational maps of threefolds after Sarkisov, J. Algebraic Geom. 4 (1995), no. 2, 223–254. MR 1311348 (96c:14013)
- Y. Hu and S. Keel, Mori dream spaces and GIT, Michigan Math. J. 48 (2000), 331–348, Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786494 (2001i:14059)
- Y. Kawamata, Flops connect minimal models, Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, 419–423. MR 2426353 (2009d:14011)
- V. V. Shokurov, $3$-fold log models, J. Math. Sci. 81 (1996), no. 3, 2667–2699, Algebraic geometry, 4. MR 1420223 (97i:14015)
Additional Information
Christopher D. Hacon
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, Utah 84112-0090
MR Author ID:
613883
Email:
hacon@math.utah.edu
James McKernan
Affiliation:
Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email:
mckernan@math.mit.edu
Received by editor(s):
September 6, 2010
Received by editor(s) in revised form:
February 18, 2011, March 22, 2011, and April 19, 2011
Published electronically:
December 12, 2012
Additional Notes:
The first author was partially supported by NSF grant no. 0757897 and by the Clay Mathematics Institute. The second author was partially supported by NSA grant no. H98230-06-1-0059, NSF grant no. 0701101 and an Eisenbud fellowship. Some of this work was done whilst both authors were visiting MSRI; both authors thank MSRI for its hospitality.
