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Boris Pasquier
Klt singularities of horospherical pairs
(Singularités klt des paires horosphériques)
Annales de l'institut Fourier, 66 no. 5 (2016), p. 2157-2167, doi: 10.5802/aif.3060
Article PDF
Class. Math.: 14E30, 14M15, 14M27
Keywords: klt pairs, flag varieties, horospherical varieties, Bott–Samelson resolutions
[1] Valery Alexeev & Michel Brion, “Stable reductive varieties. II. Projective case”, Adv. Math. 184 (2004) no. 2, p. 380-408 Article | Zbl 1080.14017
[2] Raoul Bott & Hans Samelson, “Applications of the theory of Morse to symmetric spaces”, Amer. J. Math. 80 (1958), p. 964-1029 Article | Zbl 0101.39702
[3] Michel Demazure, “Désingularisation des variétés de Schubert généralisées”, Ann. Sci. École Norm. Sup. (4) 7 (1974), p. 53-88, Collection of articles dedicated to Henri Cartan on the occasion of his 70th birthday, I Numdam | Zbl 0312.14009
[4] H. C. Hansen, “On cycles in flag manifolds”, Math. Scand. 33 (1973), p. 269-274 (1974) Zbl 0301.14019
[5] János Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 32, Springer-Verlag, Berlin, 1996 Article | Zbl 0877.14012
[6] Shrawan Kumar & Karl Schwede, “Richardson varieties have Kawamata log terminal singularities”, Int. Math. Res. Not. IMRN (2014) no. 3, p. 842-864
[7] Niels Lauritzen & Jesper Funch Thomsen, “Line bundles on Bott-Samelson varieties”, J. Algebraic Geom. 13 (2004) no. 3, p. 461-473 Article | Zbl 1080.14056
[8] Robert Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 49, Springer-Verlag, Berlin, 2004, Positivity for vector bundles, and multiplier ideals Article | Zbl 1093.14500
[9] Boris Pasquier, “Variétés horosphériques de Fano”, Bull. Soc. Math. France 136 (2008) no. 2, p. 195-225 Numdam | Zbl 1162.14030
[10] Boris Pasquier, “A survey on the singularities of spherical varieties”, http://arxiv.org/abs/1510.03995, 2015
[11] A. Ramanathan, “Schubert varieties are arithmetically Cohen-Macaulay”, Invent. Math. 80 (1985) no. 2, p. 283-294 Article | Zbl 0541.14039
Boris Pasquier
Klt singularities of horospherical pairs
(Singularités klt des paires horosphériques)
Annales de l'institut Fourier, 66 no. 5 (2016), p. 2157-2167, doi: 10.5802/aif.3060
Article PDF
Class. Math.: 14E30, 14M15, 14M27
Keywords: klt pairs, flag varieties, horospherical varieties, Bott–Samelson resolutions
Résumé - Abstract
Let $X$ be a horospherical $G$-variety and let $D$ be an effective $\mathbb{Q}$-divisor of $X$ that is stable under the action of a Borel subgroup $B$ of $G$ and such that $D+K_X$ is $\mathbb{Q}$-Cartier. We prove, using Bott–Samelson resolutions, that the pair $(X,D)$ is klt if and only if $\lfloor D\rfloor =0$.
Bibliography
[2] Raoul Bott & Hans Samelson, “Applications of the theory of Morse to symmetric spaces”, Amer. J. Math. 80 (1958), p. 964-1029 Article | Zbl 0101.39702
[3] Michel Demazure, “Désingularisation des variétés de Schubert généralisées”, Ann. Sci. École Norm. Sup. (4) 7 (1974), p. 53-88, Collection of articles dedicated to Henri Cartan on the occasion of his 70th birthday, I Numdam | Zbl 0312.14009
[4] H. C. Hansen, “On cycles in flag manifolds”, Math. Scand. 33 (1973), p. 269-274 (1974) Zbl 0301.14019
[5] János Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 32, Springer-Verlag, Berlin, 1996 Article | Zbl 0877.14012
[6] Shrawan Kumar & Karl Schwede, “Richardson varieties have Kawamata log terminal singularities”, Int. Math. Res. Not. IMRN (2014) no. 3, p. 842-864
[7] Niels Lauritzen & Jesper Funch Thomsen, “Line bundles on Bott-Samelson varieties”, J. Algebraic Geom. 13 (2004) no. 3, p. 461-473 Article | Zbl 1080.14056
[8] Robert Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 49, Springer-Verlag, Berlin, 2004, Positivity for vector bundles, and multiplier ideals Article | Zbl 1093.14500
[9] Boris Pasquier, “Variétés horosphériques de Fano”, Bull. Soc. Math. France 136 (2008) no. 2, p. 195-225 Numdam | Zbl 1162.14030
[10] Boris Pasquier, “A survey on the singularities of spherical varieties”, http://arxiv.org/abs/1510.03995, 2015
[11] A. Ramanathan, “Schubert varieties are arithmetically Cohen-Macaulay”, Invent. Math. 80 (1985) no. 2, p. 283-294 Article | Zbl 0541.14039
© Annales de L'Institut Fourier - ISSN (électronique) : 1777-5310