# 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)
• 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 ${\lfloor}D{\rfloor}=0$.

#### 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