Dense PGL-orbits in products of Grassmannians

2014/05/01 by İzzet Coşkun, Izzet Coskun, Majid Hadian +4
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG

paper · pdf · doi:10.48550/arxiv.1405.0079

21 pages

openalex publication_date 2014/05/01 · arxiv created 2015/02/02 · arxiv updated 2015/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we find some necessary and sufficient conditions on the dimension vector \underline\bfd = (d₁,..., d_k; n) so that the diagonal action of ℙGL(n) on ∏_i=1^k Gr(d_i;n) has a dense orbit. Consequently, we obtain some algorithms for finding dense and sparse dimension vectors and classify dense dimension vectors with small length or size. We also characterize the dense dimension vectors of the form (d,d,..., d; n).

Related

• \PGL orbits on products of flag varieties
• Classifying GL(n,\mathbb Z)-orbits of points and rational subspaces
• Sur la dimension de l'espace des orbites d'une grassmannienne sous l'action d'un groupe algébrique
• \mathfrakG-Quotients of Grassmannians and Equations
• Simultaneously bounded and dense orbits for commuting Cartan actions