Orbit spaces of maximal torus actions on oriented Grassmannians of planes

2018/10/01 by Hendrik Süß, Süß, Hendrik
Mathematics · #14L24 #53D20 (secondary) #57S25 (primary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1810.00981

openalex publication_date 2018/10/01 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

Motivated by Buchstaber's and Terzic' work on the complex Grassmannians G(2,4) and G(2,5) we describe the moment map and the orbit space of oriented Grassmannians of planes under the action of a maximal compact torus. Our main tool is the realisation of these oriented Grassmannians as smooth complex quadric hypersurfaces and the relatively simple Geometric Invariant Theory of the corresponding algebraic torus action.

Related

• Complex manifolds with maximal torus actions
• Toric topology of the complex Grassmann manifolds
• A resolution of singularities for the orbit spaces G_n,2/Tⁿ
• Topology of the orbit space of a maximal torus action on Gr(2,ℂ⁵)
• The smooth torus orbit closures in the Grassmannians