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Under mild conditions on Z and $\\sigma$, R is the idealizer of I in B: the maximal subring of B in which I is a two-sided ideal.\n  We give geometric conditions on Z and $\\sigma$ that determine the algebraic properties of R, and show that if Z and $\\sigma$ are sufficiently general, in a sense we make prec"},"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":"0809.3971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-23T17:22:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"346079be4c5b4e93ca3b689df704b6b99aeee8e3431467f0b5fc7e43d34ea717","abstract_canon_sha256":"770bede1b799262e0261eff4846a25b61c791a4c09750147a846e12b89ce9cb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:25.385875Z","signature_b64":"HF4ZIXHCD6jR9NqrII3Ji+ClFQg2+CcUHAp413hezdU5foOYsCgTineDwTpKNtti2UUCIYnrMOdTv3oWb/gJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bb48453ddd26f60e40e8b59f439d368cdcc48ece3e4397991b2e97d09bcaaad","last_reissued_at":"2026-05-18T04:41:25.385440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:25.385440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric idealizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Susan J. Sierra","submitted_at":"2008-09-23T17:22:55Z","abstract_excerpt":"Let X be a projective variety, $\\sigma$ an automorphism of X, L a $\\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the twisted homogeneous coordinate ring $B = B(X, L, \\sigma)$, let I be the right ideal of sections vanishing at Z. We study the subring R = k + I of B. Under mild conditions on Z and $\\sigma$, R is the idealizer of I in B: the maximal subring of B in which I is a two-sided ideal.\n  We give geometric conditions on Z and $\\sigma$ that determine the algebraic properties of R, and show that if Z and $\\sigma$ are sufficiently general, in a sense we make prec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3971","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0809.3971","created_at":"2026-05-18T04:41:25.385509+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.3971v1","created_at":"2026-05-18T04:41:25.385509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.3971","created_at":"2026-05-18T04:41:25.385509+00:00"},{"alias_kind":"pith_short_12","alias_value":"JO2IIU652JXW","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"JO2IIU652JXWBZAO","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"JO2IIU65","created_at":"2026-05-18T12:25:57.157939+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/JO2IIU652JXWBZAORNM7IOOTND","json":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND.json","graph_json":"https://pith.science/api/pith-number/JO2IIU652JXWBZAORNM7IOOTND/graph.json","events_json":"https://pith.science/api/pith-number/JO2IIU652JXWBZAORNM7IOOTND/events.json","paper":"https://pith.science/paper/JO2IIU65"},"agent_actions":{"view_html":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND","download_json":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND.json","view_paper":"https://pith.science/paper/JO2IIU65","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.3971&json=true","fetch_graph":"https://pith.science/api/pith-number/JO2IIU652JXWBZAORNM7IOOTND/graph.json","fetch_events":"https://pith.science/api/pith-number/JO2IIU652JXWBZAORNM7IOOTND/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/action/storage_attestation","attest_author":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/action/author_attestation","sign_citation":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/action/citation_signature","submit_replication":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/action/replication_record"}},"created_at":"2026-05-18T04:41:25.385509+00:00","updated_at":"2026-05-18T04:41:25.385509+00:00"}