Toric matrix Schubert varieties and their polytopes
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- by Laura Escobar and Karola Mészáros PDF
- Proc. Amer. Math. Soc. 144 (2016), 5081-5096
Abstract:
Given a matrix Schubert variety $\overline {X_\pi }$, it can be written as $\overline {X_\pi }=Y_\pi \times \mathbb {C}^q$ (where $q$ is maximal possible). We characterize when $Y_{\pi }$ is toric (with respect to a $(\mathbb {C}^*)^{2n-1}$-action) and study the associated polytope $\Phi (\mathbb {P}(Y_\pi ))$ of its projectivization. We construct regular triangulations of $\Phi (\mathbb {P}(Y_\pi ))$ which we show are geometric realizations of a family of subword complexes. Subword complexes were introduced by Knutson and Miller in 2004, who also showed that they are homeomorphic to balls or spheres and raised the question of their polytopal realizations.References
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Additional Information
- Laura Escobar
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaigh, Urbana, Illinois 61801
- MR Author ID: 990678
- ORCID: 0000-0002-7970-4152
- Email: lescobar@illinois.edu
- Karola Mészáros
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 823389
- Email: karola@math.cornell.edu
- Received by editor(s): August 23, 2015
- Received by editor(s) in revised form: February 9, 2016
- Published electronically: May 23, 2016
- Communicated by: Patricia L. Hersh
- © Copyright 2016 Laura Escobar and Karola Mészároz
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5081-5096
- MSC (2010): Primary 14M25, 52B11, 05E45
- DOI: https://doi.org/10.1090/proc/13152
- MathSciNet review: 3556254