{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ARYJKUW55F2N27QBUAP6POYOSQ","short_pith_number":"pith:ARYJKUW5","schema_version":"1.0","canonical_sha256":"04709552dde974dd7e01a01fe7bb0e940012df0966e58038cb2f1d716ab7008f","source":{"kind":"arxiv","id":"1802.06449","version":4},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.06449","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-02-18T21:21:15Z","cross_cats_sorted":[],"title_canon_sha256":"5f568a2e87d65bc0a578c8ccff55ea5b84cd9a060f7c0ce0b9b72eb55dbe7702","abstract_canon_sha256":"2e619a86bf661d27307f497c17cebd6cd4113847b1b6c869b352d451f999739e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:41.902200Z","signature_b64":"J2cBMXQY7O7M4TiBwwsd4uWttZ09ZFYerXBE7hIrKdnLFm+zgTukxGTae7E3jHpYGOtfi8PY+SYLBAtLeqptBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04709552dde974dd7e01a01fe7bb0e940012df0966e58038cb2f1d716ab7008f","last_reissued_at":"2026-05-17T23:40:41.901562Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:41.901562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.06449","created_at":"2026-05-17T23:40:41.901662+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.06449v4","created_at":"2026-05-17T23:40:41.901662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06449","created_at":"2026-05-17T23:40:41.901662+00:00"},{"alias_kind":"pith_short_12","alias_value":"ARYJKUW55F2N","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"ARYJKUW55F2N27QB","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"ARYJKUW5","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ","json":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ.json","graph_json":"https://pith.science/api/pith-number/ARYJKUW55F2N27QBUAP6POYOSQ/graph.json","events_json":"https://pith.science/api/pith-number/ARYJKUW55F2N27QBUAP6POYOSQ/events.json","paper":"https://pith.science/paper/ARYJKUW5"},"agent_actions":{"view_html":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ","download_json":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ.json","view_paper":"https://pith.science/paper/ARYJKUW5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.06449&json=true","fetch_graph":"https://pith.science/api/pith-number/ARYJKUW55F2N27QBUAP6POYOSQ/graph.json","fetch_events":"https://pith.science/api/pith-number/ARYJKUW55F2N27QBUAP6POYOSQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ/action/storage_attestation","attest_author":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ/action/author_attestation","sign_citation":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ/action/citation_signature","submit_replication":"https://pith.science/pith/ARYJKUW55F2N27QBUAP6POYOSQ/action/replication_record"}},"created_at":"2026-05-17T23:40:41.901662+00:00","updated_at":"2026-05-17T23:40:41.901662+00:00"}