Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SINGULARITIES OF DIVISORS ON FLAG VARIETIES VIA HWANG'S PRODUCT THEOREM

  • Smirnov, Evgeny (Faculty of Mathematics and Laboratory of Algebraic Geometry and its Applications National Research University Higher School of Economics)
  • Received : 2016.09.19
  • Accepted : 2017.02.13
  • Published : 2017.09.30

Abstract

We give an alternative proof of a recent result by B. Pasquier stating that for a generalized flag variety X = G/P and an effective ${\mathbb{Q}}-divisor$ D stable with respect to a Borel subgroup the pair (X, D) is Kawamata log terminal if and only if ${\lfloor}D{\rfloor}=0$.

Keywords

File

Download PDF

References

  1. M. Brion, Curves and divisors in spherical varieties, In Algebraic groups and Lie groups, volume 9 of Austral. Math. Soc. Lect. Ser., pages 21-34. Cambridge Univ. Press, Cambridge, 1997.
  2. M. Brion, Lectures on the geometry of ag varieties, In Topics in cohomological studies of algebraic varieties, Trends Math., pages 33-85. Birkhauser, Basel, 2005.
  3. I. A. Chel'tsov and K. A. Shramov, Log-canonical thresholds for nonsingular Fano three-folds, with an appendix by J.-P.Demailly, Uspekhi Mat. Nauk 63 (2008), no. 5, 73-180.
  4. J.-M. Hwang, Log canonical thresholds of divisors on Grassmannians, Math. Ann. 334 (2006), no. 2, 413-418. https://doi.org/10.1007/s00208-005-0731-6
  5. J.-M. Hwang, Log canonical thresholds of divisors on Fano manifolds of Picard number 1, Compos. Math. 143 (2007), no. 1, 89-94. https://doi.org/10.1112/S0010437X06002454
  6. J. Kollar, Singularities of pairs, In Algebraic geometry-Santa Cruz 1995, volume 62 of Proc. Sympos. Pure Math., pages 221-287. Amer. Math. Soc., Providence, RI, 1997.
  7. B. Pasquier, Klt singularities of horospherical pairs, Ann. Inst. Fourier (Grenoble) 66 (2016), no. 5, 2157-2167. https://doi.org/10.5802/aif.3060