\PGL orbits on products of flag varieties

2024/12/06 by Coskun, Izzet, Gündüz, Abuzer
#14L30 #14L35 #14M15 #14M17 #51N30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.04870

Abstract

In this paper, we study the existence of a dense orbit for the diagonal \PGL(n) action on self-products of partial flag varieties. We determine when there exists a dense orbit for flag varieties of the form F(k₁, …, k_r; n)^m when k_i = i or when m=3 and k_i = ℓ + i for some ℓ ≥ 0. We also show that certain infinite families of products do not have a dense orbit.

Related

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• Diagonal Orbits in a Type A Double Flag Variety of Complexity One
• Multiple Flag Varieties of Finite Type
• Dense PGL-orbits in products of Grassmannians
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