On Schubert varieties of complexity one

Abstract

Let $B$ be a Borel subgroup of ${\mathrm{GL}}_n(\mathbb{C})$ and $\mathbb{T}$ a maximal torus contained in $B$. Then $\mathbb{T}$ acts on ${\mathrm{GL}}_n(\mathbb{C})/B$ 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 $k$. In this paper, we discuss topology, geometry, and combinatorics related to Schubert varieties of complexity one.

arXiv comment24 pages, 4 figures

References in corpus (6)

• Generic torus orbit closures in Schubert varieties
• Toric Bruhat interval polytopes
• Rhombic tilings and Bott-Samelson varieties
• Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold
• Flag Bott manifolds of general Lie type and their equivariant cohomology rings
• Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations