Geodesic
Multiple Flag Varieties
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 147 (2018), pp. 84-119.

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This paper is a review of results on multiple flag varieties, i.e., varieties of the form $G/P_1\times\dots\times G/P_r$. We provide a classification of multiple flag varieties of complexity $0$ and $1$ and results on the combinatorics and geometry of $B$-orbits and their closures in double cominuscule flag varieties. We also discuss questions of finiteness for the number of $G$-orbits and existence of an open $G$-orbits on a multiple flag variety.
Keywords: flag varieties, spherical varieties. 
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E. Yu. Smirnov. Multiple Flag Varieties. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 147 (2018), pp. 84-119. http://geodesic.mathdoc.fr/item/INTO_2018_147_a2/

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