{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FF2X7TUMGY4AYDKEOVNYMCSPB4","short_pith_number":"pith:FF2X7TUM","schema_version":"1.0","canonical_sha256":"29757fce8c36380c0d44755b860a4f0f08d334115d9efc3ec71a66dce245ace1","source":{"kind":"arxiv","id":"1203.6126","version":2},"attestation_state":"computed","paper":{"title":"Richardson Varieties Have Kawamata Log Terminal Singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Karl Schwede, Shrawan Kumar","submitted_at":"2012-03-28T01:29:13Z","abstract_excerpt":"Let $X^v_w$ be a Richardson variety in the full flag variety $X$ associated to a symmetrizable Kac-Moody group $G$. Recall that $X^v_w$ is the intersection of the finite dimensional Schubert variety $X_w$ with the finite codimensional opposite Schubert variety $X^v$. We give an explicit $\\bQ$-divisor $\\Delta$ on $X^v_w$ and prove that the pair $(X^v_w, \\Delta)$ has Kawamata log terminal singularities. In fact, $-K_{X^v_w} - \\Delta$ is ample, which additionally proves that $(X^v_w, \\Delta)$ is log Fano.\n  We first give a proof of our result in the finite case (i.e., in the case when $G$ is a fi"},"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":"1203.6126","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-28T01:29:13Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7d0560fd3a9e6a2a261d55f7faf2af5bbb0c20bfaa7586228a416541d1947cc3","abstract_canon_sha256":"21700f1340b6fd9d76d993f6721cdd6343509ed24c720cf49f6a7ca620f717e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.121288Z","signature_b64":"4dD5vfseTeXbRMKqPhLlSBaTV7Ju96BdEfwEWmdH0aoPPxaFTLfw5z1PZR2KB1McNiCQdJNtjlatmaCsEVQ5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29757fce8c36380c0d44755b860a4f0f08d334115d9efc3ec71a66dce245ace1","last_reissued_at":"2026-05-18T02:57:45.120867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.120867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Richardson Varieties Have Kawamata Log Terminal Singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Karl Schwede, Shrawan Kumar","submitted_at":"2012-03-28T01:29:13Z","abstract_excerpt":"Let $X^v_w$ be a Richardson variety in the full flag variety $X$ associated to a symmetrizable Kac-Moody group $G$. Recall that $X^v_w$ is the intersection of the finite dimensional Schubert variety $X_w$ with the finite codimensional opposite Schubert variety $X^v$. We give an explicit $\\bQ$-divisor $\\Delta$ on $X^v_w$ and prove that the pair $(X^v_w, \\Delta)$ has Kawamata log terminal singularities. In fact, $-K_{X^v_w} - \\Delta$ is ample, which additionally proves that $(X^v_w, \\Delta)$ is log Fano.\n  We first give a proof of our result in the finite case (i.e., in the case when $G$ is a fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6126","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":"1203.6126","created_at":"2026-05-18T02:57:45.120931+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.6126v2","created_at":"2026-05-18T02:57:45.120931+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6126","created_at":"2026-05-18T02:57:45.120931+00:00"},{"alias_kind":"pith_short_12","alias_value":"FF2X7TUMGY4A","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FF2X7TUMGY4AYDKE","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FF2X7TUM","created_at":"2026-05-18T12:27:06.952714+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/FF2X7TUMGY4AYDKEOVNYMCSPB4","json":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4.json","graph_json":"https://pith.science/api/pith-number/FF2X7TUMGY4AYDKEOVNYMCSPB4/graph.json","events_json":"https://pith.science/api/pith-number/FF2X7TUMGY4AYDKEOVNYMCSPB4/events.json","paper":"https://pith.science/paper/FF2X7TUM"},"agent_actions":{"view_html":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4","download_json":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4.json","view_paper":"https://pith.science/paper/FF2X7TUM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.6126&json=true","fetch_graph":"https://pith.science/api/pith-number/FF2X7TUMGY4AYDKEOVNYMCSPB4/graph.json","fetch_events":"https://pith.science/api/pith-number/FF2X7TUMGY4AYDKEOVNYMCSPB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4/action/storage_attestation","attest_author":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4/action/author_attestation","sign_citation":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4/action/citation_signature","submit_replication":"https://pith.science/pith/FF2X7TUMGY4AYDKEOVNYMCSPB4/action/replication_record"}},"created_at":"2026-05-18T02:57:45.120931+00:00","updated_at":"2026-05-18T02:57:45.120931+00:00"}