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

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      https://www.ias.ac.in/article/fulltext/pmsc/119/04/0469-0485

    • Keywords

       

      Semistable points; line bundle; coxeter element.

    • Abstract

       

      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 $X(\tau)$ admits a semistable point for the action of the torus 𝑇 with respect to a non-trivial line bundle on $G/B$.

    • Author Affiliations

       

      S S Kannan1 S K Pattanayak1

      1. Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur Post Office, Siruseri 603 103, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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