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Threefold thresholds

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Abstract.

We prove that the set of accumulation points of thresholds in dimension three is equal to the set of thresholds in dimension two, excluding one.

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References

  1. Alexeev, V.: Boundedness and K2 for log surfaces. Int. J. Math. 5, 779–810 (1994)

    MathSciNet  MATH  Google Scholar 

  2. Alexeev, V., Brion, M.: Boundedness of spherical Fano varieties. To appear in the Proceeding of the Fano Conference, Torino, October 2002, arXiv:math.AG/0301196

  3. Borisov, A.A., Borisov, L.A.: Singular toric Fano three-folds. Mat. Sb. 183 (2), 134–141 (1992)

    MATH  Google Scholar 

  4. Cheltsov, I.: Log canonical thresholds on hypersurfaces. Mat. Sb. 192 (8), 155–172 (2001)

    MATH  Google Scholar 

  5. Cheltsov, I., Park, J.: Global log-canonical thresholds and generalized Eckardt points. Mat. Sb. 193 (5), 149–160 (2002)

    Google Scholar 

  6. Corti, A.: Threefold flips after Shokurov

  7. de Fernex, T., Ein, L., Mustata, M.: Bounds for log canonical thresholds with applications to birational rigidity. arXiv:math.AG/0212211

  8. de Fernex, T., Ein, L., Mustata, M.: Multiplicities and log canonical threshold. arXiv:math.AG/0205171

  9. Ein, L., Mustata, M.: The log canonical threshold of homogeneous affine hypersurfaces. arXiv:math.AG/0105113

  10. Graber, T., Harris, J., Starr, J.: Families of rationally connected varieties. J. Am. Math. Soc. 16 (1), 57–67 (2003) (electronic)

    Article  MATH  Google Scholar 

  11. Hassett, B.: Moduli spaces of weighted pointed stable curves. arXiv:math. AG/0205009

  12. Hu, Y., Keel, S.: Mori dream spaces and GIT, Dedicated to William Fulton on the occasion of his 60th birthday. Michigan Math. J. 48, 331–348 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Igusa, J.: On the first terms of certain asymptotic expansions. In: Complex analysis and algebraic geometry, Tokyo, Iwanami Shoten, 1977, pp. 357–368

  14. Ishii, S.: Log canonical thresholds for pairs Cn and non-degenerate hypersurfaces. Unpublished

  15. Kawamata, Y.: Boundedness of Q-Fano threefolds, Proceedings of the International Conference on Algebra. Part 3 (Novosibirsk, 1989), Contemp. Math., Amer. Math. Soc., Providence, RI, 131, 439–445 (1992)

    MATH  Google Scholar 

  16. Kollár, J.: Log Surfaces of General type; some conjectures. Contemp. Math. 162, 261–275 (1994)

    Google Scholar 

  17. Kollár, J.: Rational Curves on Algebraic Varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete, 32, Springer, 1996

  18. Kollár, J.: Singularities of pairs. Algebraic geometry–Santa Cruz 1995, Amer. Math. Soc., Providence, RI, 1997, pp. 221–287

  19. Kollár, J., et~al.: Flips and abundance for algebraic threefolds. Société Mathématique de France, Paris, 1992 Papers from the Second Summer Seminar on Algebraic Geometry held at the University of Utah, Salt Lake City, Utah, August 1991, Astérisque No. 211, 1992

  20. Kollár, J., Miyaoka, Y., Mori, S.: Rationally Connected Varieties. J. Algebraic Geometry 1, 429–448 (1992)

    MathSciNet  Google Scholar 

  21. Kollár, J., Miyaoka, Y., Mori, S., Takagi, H.: Boundedness of canonical Q-Fano 3-folds. Proc. Japan Acad. Ser. A Math. Sci. 76 (5), 73–77 (2000)

    Google Scholar 

  22. Kuwata, T.: On log canonical thresholds of surfaces in ℂ3. Tokyo J. Math. 22 (1), 245–251 (1999)

    MATH  Google Scholar 

  23. Kuwata, T.: On log canonical thresholds of reducible plane curves. Am. J. Math. 121 (4), 701–721 (1999)

    MATH  Google Scholar 

  24. Prokhorov, Yu., G.: On log canonical thresholds I. Commun. Algebra 29 (9), 3961–3970 (2001)

    Article  MATH  Google Scholar 

  25. Prokhorov, Yu., G.: On log canonical thresholds II. Commun. Algebra 30 (12), 5809–5823 (2002)

    Article  MATH  Google Scholar 

  26. Pukhlikov, A.V.: Birationally rigid Fano hypersurfaces. arXiv:math.AG/0201302

  27. Shokurov, V.V.: 3-fold log models, Algebraic geometry, 4. J. Math. Sci. 81 (3), 2667–2699 (1996)

    MATH  Google Scholar 

  28. Shokurov, V.V.: Prelimiting flips. Proc. Steklov Inst. of Math. 240, 82–219 (2003)

    Google Scholar 

  29. Shokurov, V. V.: Letters of a Bi-Rationalist V. Mld’s and termination of log flips. Proc. Steklov Inst. of Math., 2004, To appear

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Authors and Affiliations

  1. Department of Mathematics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA

    James McKernan

  2. Department of Algebra, Faculty of Mathematics, Moscow State Lomonosov University, Leninskie Gory, GSP-2, Moscow, 119 992, Russia

    Yuri Prokhorov

Authors
  1. James McKernan
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  2. Yuri Prokhorov
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Correspondence to James McKernan.

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McKernan, J., Prokhorov, Y. Threefold thresholds. manuscripta math. 114, 281–304 (2004). https://doi.org/10.1007/s00229-004-0457-x

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  • DOI: https://doi.org/10.1007/s00229-004-0457-x

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