Projective normality of torus quotients of flag varieties

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Nayek, Arpita¹  Pattanayak, S. K.¹  Jindal, Shivang¹ 

[1] Indian Inst Technol, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

关键词: Projective normality;    Grassmannian;    Semi-stable point;    Line bundle;   

DOI  :  10.1016/j.jpaa.2020.106389

来源: Elsevier

【 摘 要 】

Let G = SLn (C) and T be a maximal torus in G. We show that the quotient T\\G/P-alpha 1 boolean AND P-alpha 2 is projectively normal with respect to the descent of a suitable line bundle, where P t is the maximal parabolic subgroup in G associated to the simple root alpha(i), i = 1, 2. We give a degree bound of the generators of the homogeneous coordinate ring of T\\(G(3,6))(T)(ss)(L-2 (omega) over bar3). If G = Spin(7), we give a degree bound of the generators of the homogeneous coordinate ring of T\\(G/P-alpha 2)(T)(ss) (L-2 (omega) over bar2) whereas we prove that the quotient T\\(G/P-alpha 3)(T)(ss) (L-4 (omega) over bar3)) is projectively normal with respect to the descent of the line bundles L-4 (omega) over bar(3). (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free