{"paper":{"title":"Toric topology of the complex Grassmann manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Svjetlana Terzic, Victor M. Buchstaber","submitted_at":"2018-02-18T21:21:15Z","abstract_excerpt":"The family of the complex Grassmann manifolds $G_{n,k}$ with a canonical action of the torus $T^n=\\mathbb{T}^{n}$ and the analogue of the moment map $\\mu : G_{n,k}\\to \\Delta _{n,k}$ for the hypersimplex $\\Delta _{n,k}$, is well known. In this paper we study the structure of the orbit space $G_{n,k}/T^n$ by developing the methods of toric geometry and toric topology. We use a subdivision of $G_{n,k}$ into the strata $W_{\\sigma}$ and determine all regular and singular points of the moment map $\\mu$, introduce the notion of the admissible polytopes $P_\\sigma$ such that $\\mu (W_{\\sigma}) = \\stackr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06449","kind":"arxiv","version":4},"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"}