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Upper bound of the multiplicity of a Du Bois singularity

Author: Kohsuke Shibata
Journal: Proc. Amer. Math. Soc. 145 (2017), 1053-1059
MSC (2010): Primary 13H15; Secondary 14B05
Published electronically: September 29, 2016
MathSciNet review: 3589305
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Abstract: This paper answers in the affirmative a question raised by Huneke and Watanabe concerning an upper bound on the multiplicity of a normal Cohen-Macaulay Du Bois singularity.

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  • [1] Robin Hartshorne, Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. MR 0222093
  • [2] Craig Huneke and Kei-ichi Watanabe, Upper bound of multiplicity of F-pure rings, Proc. Amer. Math. Soc. 143 (2015), no. 12, 5021-5026. MR 3411123,
  • [3] Eero Hyry and Karen E. Smith, On a non-vanishing conjecture of Kawamata and the core of an ideal, Amer. J. Math. 125 (2003), no. 6, 1349-1410. MR 2018664
  • [4] Shihoko Ishii, Introduction to singularities, Springer, Tokyo, 2014. MR 3288750
  • [5] János Kollár and Sándor J. Kovács, Log canonical singularities are Du Bois, J. Amer. Math. Soc. 23 (2010), no. 3, 791-813. MR 2629988,
  • [6] 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
  • [7] Sándor J. Kovács, Karl Schwede, and Karen E. Smith, The canonical sheaf of Du Bois singularities, Adv. Math. 224 (2010), no. 4, 1618-1640. MR 2646306,
  • [8] Henry B. Laufer, On minimally elliptic singularities, Amer. J. Math. 99 (1977), no. 6, 1257-1295. MR 0568898
  • [9] Judith D. Sally, Cohen-Macaulay local rings of maximal embedding dimension, J. Algebra 56 (1979), no. 1, 168-183. MR 527163,
  • [10] Karl Schwede, A simple characterization of Du Bois singularities, Compos. Math. 143 (2007), no. 4, 813-828. MR 2339829,
  • [11] J. H. M. Steenbrink, Mixed Hodge structures associated with isolated singularities, Singularities, Part 2 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 513-536. MR 713277

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Additional Information

Kohsuke Shibata
Affiliation: Graduate school of Mathematical Science, University of Tokyo, 3-8-1 Komaba, Meguro, 153-8914, Tokyo, Japan

Received by editor(s): April 14, 2016
Received by editor(s) in revised form: May 3, 2016, and May 16, 2016
Published electronically: September 29, 2016
Additional Notes: The author was partially supported by JSPS KAKENHI Grant Number 15-J09158
Communicated by: Irena Peeva
Article copyright: © Copyright 2016 American Mathematical Society

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