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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 mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Existence of minimal models for varieties of log general type II
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by Christopher D. Hacon and James M$^{\mathrm {c}}$Kernan
J. Amer. Math. Soc. 23 (2010), 469-490
DOI: https://doi.org/10.1090/S0894-0347-09-00651-1
Published electronically: November 13, 2009
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Abstract:

Assuming finite generation in dimension $n-1$, we prove that pl-flips exist in dimension $n$.
References
  • Florin Ambro, Restrictions of log canonical algebras of general type, J. Math. Sci. Univ. Tokyo 13 (2006), no. 3, 409–437. MR 2284409
  • C. Birkar, P. Cascini, C. Hacon, and J. McKernan, Existence of minimal models for varieties of log general type. J. Amer. Math. Soc., posted on November 13, 2009, PII: S 0894-0347(09)00649-3.
  • Alessio Corti, 3-fold flips after Shokurov, Flips for 3-folds and 4-folds, Oxford Lecture Ser. Math. Appl., vol. 35, Oxford Univ. Press, Oxford, 2007, pp. 18–48. MR 2359340, DOI 10.1093/acprof:oso/9780198570615.003.0002
  • Lawrence Ein, Robert Lazarsfeld, Mircea Mustaţă, Michael Nakamaye, and Mihnea Popa, Asymptotic invariants of base loci, Ann. Inst. Fourier (Grenoble) 56 (2006), no. 6, 1701–1734 (English, with English and French summaries). MR 2282673
  • Christopher D. Hacon and James McKernan, Boundedness of pluricanonical maps of varieties of general type, Invent. Math. 166 (2006), no. 1, 1–25. MR 2242631, DOI 10.1007/s00222-006-0504-1
  • Alessio Corti (ed.), Flips for 3-folds and 4-folds, Oxford Lecture Series in Mathematics and its Applications, vol. 35, Oxford University Press, Oxford, 2007. MR 2352762, DOI 10.1093/acprof:oso/9780198570615.001.0001
  • Yujiro Kawamata, On the extension problem of pluricanonical forms, Algebraic geometry: Hirzebruch 70 (Warsaw, 1998) Contemp. Math., vol. 241, Amer. Math. Soc., Providence, RI, 1999, pp. 193–207. MR 1718145, DOI 10.1090/conm/241/03636
  • János Kollár and Shigefumi Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998. With the collaboration of C. H. Clemens and A. Corti; Translated from the 1998 Japanese original. MR 1658959, DOI 10.1017/CBO9780511662560
  • Robert Lazarsfeld, Positivity in algebraic geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48, Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. MR 2095471, DOI 10.1007/978-3-642-18808-4
  • Robert Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 49, Springer-Verlag, Berlin, 2004. Positivity for vector bundles, and multiplier ideals. MR 2095472, DOI 10.1007/978-3-642-18808-4
  • Noboru Nakayama, Zariski-decomposition and abundance, MSJ Memoirs, vol. 14, Mathematical Society of Japan, Tokyo, 2004. MR 2104208
  • V. V. Shokurov, Prelimiting flips, Tr. Mat. Inst. Steklova 240 (2003), no. Biratsion. Geom. Lineĭn. Sist. Konechno Porozhdennye Algebry, 82–219; English transl., Proc. Steklov Inst. Math. 1(240) (2003), 75–213. MR 1993750
  • Y-T. Siu, A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring. arXiv:math.AG/0610740
  • Yum-Tong Siu, Invariance of plurigenera, Invent. Math. 134 (1998), no. 3, 661–673. MR 1660941, DOI 10.1007/s002220050276
  • Endre Szabó, Divisorial log terminal singularities, J. Math. Sci. Univ. Tokyo 1 (1994), no. 3, 631–639. MR 1322695
  • Shigeharu Takayama, Pluricanonical systems on algebraic varieties of general type, Invent. Math. 165 (2006), no. 3, 551–587. MR 2242627, DOI 10.1007/s00222-006-0503-2
  • H. Tsuji, Pluricanonical systems of projective varieties of general type. arXiv:math.AG/ 9909021
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Bibliographic Information
  • 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 M$^{\mathrm {c}}$Kernan
  • 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 NSF research grant no. 0456363 and an AMS Centennial fellowship.
    The second author was partially supported by NSA grant no. H98230-06-1-0059 and NSF grant no. 0701101
    The authors would like to thank F. Ambro, C. Birkar, P. Cascini, J. A. Chen, A. Corti, O. Fujino, S. Keel, J. Kollár and the referee for valuable suggestions.
  • © 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), 469-490
  • MSC (2010): Primary 14E30
  • DOI: https://doi.org/10.1090/S0894-0347-09-00651-1
  • MathSciNet review: 2601040