{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:D7MEY2MTNXZP6NQZJ6BOT47QKC","short_pith_number":"pith:D7MEY2MT","schema_version":"1.0","canonical_sha256":"1fd84c69936df2ff36194f82e9f3f050a45a8124cc6a56af11a958d31538a2fd","source":{"kind":"arxiv","id":"1101.0352","version":2},"attestation_state":"computed","paper":{"title":"Equivariant Chow cohomology of nonsimplicial toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hal Schenck","submitted_at":"2011-01-01T16:52:45Z","abstract_excerpt":"For a toric variety X_P determined by a rational polyhedral fan P in a lattice N, Payne shows that the equivariant Chow cohomology of X_P is the Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use the Cartan-Eilenberg spectral sequence to analyze the associated reflexive sheaf on Proj(N), showing that the Chern classes depend on subtle geometry of P and giving criteria for the splitting of the sheaf as a sum of line bundles. For certain fans associated to the reflection arrangement A_n, we describe a connection between C^0(P) and logarithmic vector fields tangent to "},"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":"1101.0352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-01T16:52:45Z","cross_cats_sorted":[],"title_canon_sha256":"474d8d404ec8e8abc9b2d3264b6ad2eb2fbcdc7b02fbe0cdd9b4a6cd17043d8f","abstract_canon_sha256":"ecec7f33098b92f9b5de70aa2e99913996ae844df6ecff64fa250f95def2630b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.294351Z","signature_b64":"Wt5TQuuWYRz92OaDWK5pRm7YGehCCsHinXPecebmpwaItsukhbXIkw0LxImi3c1by3/XYvnWNkiBhajjW91hAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fd84c69936df2ff36194f82e9f3f050a45a8124cc6a56af11a958d31538a2fd","last_reissued_at":"2026-05-18T02:47:53.293816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.293816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivariant Chow cohomology of nonsimplicial toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hal Schenck","submitted_at":"2011-01-01T16:52:45Z","abstract_excerpt":"For a toric variety X_P determined by a rational polyhedral fan P in a lattice N, Payne shows that the equivariant Chow cohomology of X_P is the Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use the Cartan-Eilenberg spectral sequence to analyze the associated reflexive sheaf on Proj(N), showing that the Chern classes depend on subtle geometry of P and giving criteria for the splitting of the sheaf as a sum of line bundles. For certain fans associated to the reflection arrangement A_n, we describe a connection between C^0(P) and logarithmic vector fields tangent to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0352","kind":"arxiv","version":2},"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":"1101.0352","created_at":"2026-05-18T02:47:53.293901+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.0352v2","created_at":"2026-05-18T02:47:53.293901+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0352","created_at":"2026-05-18T02:47:53.293901+00:00"},{"alias_kind":"pith_short_12","alias_value":"D7MEY2MTNXZP","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"D7MEY2MTNXZP6NQZ","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"D7MEY2MT","created_at":"2026-05-18T12:26:26.731475+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/D7MEY2MTNXZP6NQZJ6BOT47QKC","json":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC.json","graph_json":"https://pith.science/api/pith-number/D7MEY2MTNXZP6NQZJ6BOT47QKC/graph.json","events_json":"https://pith.science/api/pith-number/D7MEY2MTNXZP6NQZJ6BOT47QKC/events.json","paper":"https://pith.science/paper/D7MEY2MT"},"agent_actions":{"view_html":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC","download_json":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC.json","view_paper":"https://pith.science/paper/D7MEY2MT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.0352&json=true","fetch_graph":"https://pith.science/api/pith-number/D7MEY2MTNXZP6NQZJ6BOT47QKC/graph.json","fetch_events":"https://pith.science/api/pith-number/D7MEY2MTNXZP6NQZJ6BOT47QKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC/action/storage_attestation","attest_author":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC/action/author_attestation","sign_citation":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC/action/citation_signature","submit_replication":"https://pith.science/pith/D7MEY2MTNXZP6NQZJ6BOT47QKC/action/replication_record"}},"created_at":"2026-05-18T02:47:53.293901+00:00","updated_at":"2026-05-18T02:47:53.293901+00:00"}