Torus Quotients of Homogeneous Spaces - Minimal Dimensional Schubert Varieties Admitting Semi-Stable Points

Proceedings Mathematical Sciences

S S Kannan²  S K Pattanayak¹ 

[1] $$;Chennai Mathematical Institute, Plot H, SIPCOT IT Park, Padur Post Office, Siruseri 0 0, India$$

关键词: Semistable points;    line bundle;    coxeter element.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, for any simple, simply connected algebraic group 𝐺 of type 𝐵,𝐶 or 𝐷 and for any maximal parabolic subgroup 𝑃 of 𝐺, we describe all minimal dimensional Schubert varieties in $G/P$ admitting semistable points for the action of a maximal torus 𝑇 with respect to an ample line bundle on $G/P$. We also describe, for any semi-simple simply connected algebraic group 𝐺 and for any Borel subgroup 𝐵 of 𝐺, all Coxeter elements 𝜏 for which the Schubert variety 𝑋(𝜏) admits a semistable point for the action of the torus 𝑇 with respect to a non-trivial line bundle on 𝐺/𝐵 .

【 授权许可】

Unknown