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Schubert varieties are log Fano over the integers


Authors: Dave Anderson and Alan Stapledon
Journal: Proc. Amer. Math. Soc. 142 (2014), 409-411
MSC (2010): Primary 14M15; Secondary 14E30, 20G99
DOI: https://doi.org/10.1090/S0002-9939-2013-11779-X
Published electronically: November 4, 2013
MathSciNet review: 3133983
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a Schubert variety $ X_w$, we exhibit a divisor $ \Delta $, defined over $ \mathbb{Z}$, such that the pair $ (X_w,\Delta )$ is log Fano in all characteristics.


References [Enhancements On Off] (What's this?)

  • [1] C. Chevalley, Sur les décompositions cellulaires des espaces $ G/B$, with a foreword by Armand Borel, Proc. Sympos. Pure Math., vol. 56, Amer. Math. Soc., Providence, RI, 1994, pp. 1-23 (French). MR 1278698 (95e:14041)
  • [2] János Kollár and Shigefumi Mori, Birational geometry of algebraic varieties, with the collaboration of C. H. Clemens and A. Corti, translated from the 1998 Japanese original, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998. MR 1658959 (2000b:14018)
  • [3] Niels Lauritzen, Ulf Raben-Pedersen, and Jesper Funch Thomsen, Global $ F$-regularity of Schubert varieties with applications to $ \mathcal {D}$-modules, J. Amer. Math. Soc. 19 (2006), no. 2, 345-355 (electronic). MR 2188129 (2006h:14005), https://doi.org/10.1090/S0894-0347-05-00509-6
  • [4] V. B. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. of Math. (2) 122 (1985), no. 1, 27-40. MR 799251 (86k:14038), https://doi.org/10.2307/1971368
  • [5] A. Ramanathan, Schubert varieties are arithmetically Cohen-Macaulay, Invent. Math. 80 (1985), no. 2, 283-294. MR 788411 (87d:14044), https://doi.org/10.1007/BF01388607
  • [6] Karl Schwede and Karen E. Smith, Globally $ F$-regular and log Fano varieties, Adv. Math. 224 (2010), no. 3, 863-894. MR 2628797 (2011e:14076), https://doi.org/10.1016/j.aim.2009.12.020

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Additional Information

Dave Anderson
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: dandersn@math.washington.edu

Alan Stapledon
Affiliation: Department of Mathematics, University of British Columbia, BC, Canada V6T 1Z2
Email: astapldn@math.ubc.ca

DOI: https://doi.org/10.1090/S0002-9939-2013-11779-X
Received by editor(s): March 8, 2011
Received by editor(s) in revised form: March 8, 2012, and March 27, 2012
Published electronically: November 4, 2013
Additional Notes: The first author was partially supported by NSF Grant DMS-0902967
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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