#### Vol. 315, No. 2, 2021

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On Schubert varieties of complexity one

### Eunjeong Lee, Mikiya Masuda and Seonjeong Park

Vol. 315 (2021), No. 2, 419–447
DOI: 10.2140/pjm.2021.315.419
##### Abstract

Let $B$ be a Borel subgroup of ${GL}_{n}\left(ℂ\right)$ and $\mathbb{𝕋}$ a maximal torus contained in $B$. Then $\mathbb{𝕋}$ acts on ${GL}_{n}\left(ℂ\right)∕B$ and every Schubert variety is $\mathbb{𝕋}$-invariant. We say that a Schubert variety is of complexity $k$ if a maximal $\mathbb{𝕋}$-orbit in ${X}_{w}$ has codimension $k$. We discuss topology, geometry, and combinatorics related to Schubert varieties of complexity one.

##### Keywords
Schubert varieties, torus action, pattern avoidance, flag Bott–Samelson varieties, flag Bott manifolds
##### Mathematical Subject Classification
Primary: 14M15, 14M25
Secondary: 05A05