{"paper":{"title":"Toric matrix Schubert varieties and their polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Karola Meszaros, Laura Escobar","submitted_at":"2015-08-14T09:18:19Z","abstract_excerpt":"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 ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03445","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}