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arXiv · 2307.09265

PGL orbits in tree varieties

Izzet Coskun·Demir Eken·Chris Yun
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Abstract

In this paper, we introduce tree varieties as a natural generalization of products of partial flag varieties. We study orbits of the PGL action on tree varieties. We characterize tree varieties with finitely many PGL orbits, generalizing a celebrated theorem of Magyar, Weyman and Zelevinsky. We give criteria that guarantee that a tree variety has a dense PGL orbit and provide many examples of tree varieties that do not have dense PGL orbits. We show that a triple of two-step flag varieties $F(k_1, k_2; n)^3$ has a dense PGL orbit if and only if $k_1 + k_2 \not= n$.

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Izzet Coskun, Demir Eken, Chris Yun. 2023-07-18. PGL orbits in tree varieties. https://arxiv.org/abs/2307.09265

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