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 GLn() and 𝕋 a maximal torus contained in B. Then 𝕋 acts on GLn()B and every Schubert variety is 𝕋-invariant. We say that a Schubert variety is of complexity k if a maximal 𝕋-orbit in Xw 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
Milestones
Received: 8 October 2020
Revised: 16 July 2021
Accepted: 11 October 2021
Published: 19 January 2022
Authors
Eunjeong Lee
Center for Geometry and Physics
Institute for Basic Science (IBS)
Pohang
South Korea
Mikiya Masuda
Department of Mathematics
Osaka City University
Osaka
Japan
Seonjeong Park
Department of Mathematics Education
Jeonju University
Jeonju
South Korea