{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:XU6MUU55TKVBFQMSM62C3TMMWU","short_pith_number":"pith:XU6MUU55","schema_version":"1.0","canonical_sha256":"bd3cca53bd9aaa12c19267b42dcd8cb53e7f320b0eb9de0c9e3d0bb815d96364","source":{"kind":"arxiv","id":"0811.0626","version":2},"attestation_state":"computed","paper":{"title":"Canonical divisors on T-varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hendrik S\\\"u{\\ss}","submitted_at":"2008-11-05T08:45:13Z","abstract_excerpt":"Generalising toric geometry we study compact varieties admitting lower dimensional torus actions. In particular we describe divisors on them in terms of convex geometry and give a criterion for their ampleness. These results may be used to study Fano varieties with small torus actions. As a first result we classify log del Pezzo C*-surfaces of Picard number 1 and Gorenstein index less than 4. In further examples we show how classification might work in higher dimensions and we give explicit descriptions of some equivariant smoothings of Fano threefolds."},"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":"0811.0626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-11-05T08:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"786e3a35f1ae15a848b9fe13df6e1e24be2158f508d8915622a6488b4006fe24","abstract_canon_sha256":"d476059362c26b72bcedd059c32fa0d79853be922bd45e4b175a607c7d3df7f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:18.291770Z","signature_b64":"muXFSRXNG35s/9tQRuCHPbwExrtTSQ/Ko8osL03YgSrU169dWfD/5Q0gLYyTnWi/mWD17WLc94Lam7ry9LoiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd3cca53bd9aaa12c19267b42dcd8cb53e7f320b0eb9de0c9e3d0bb815d96364","last_reissued_at":"2026-05-18T04:33:18.291107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:18.291107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical divisors on T-varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hendrik S\\\"u{\\ss}","submitted_at":"2008-11-05T08:45:13Z","abstract_excerpt":"Generalising toric geometry we study compact varieties admitting lower dimensional torus actions. In particular we describe divisors on them in terms of convex geometry and give a criterion for their ampleness. These results may be used to study Fano varieties with small torus actions. As a first result we classify log del Pezzo C*-surfaces of Picard number 1 and Gorenstein index less than 4. In further examples we show how classification might work in higher dimensions and we give explicit descriptions of some equivariant smoothings of Fano threefolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0626","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":"0811.0626","created_at":"2026-05-18T04:33:18.291231+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.0626v2","created_at":"2026-05-18T04:33:18.291231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0626","created_at":"2026-05-18T04:33:18.291231+00:00"},{"alias_kind":"pith_short_12","alias_value":"XU6MUU55TKVB","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"XU6MUU55TKVBFQMS","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"XU6MUU55","created_at":"2026-05-18T12:25:58.018023+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/XU6MUU55TKVBFQMSM62C3TMMWU","json":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU.json","graph_json":"https://pith.science/api/pith-number/XU6MUU55TKVBFQMSM62C3TMMWU/graph.json","events_json":"https://pith.science/api/pith-number/XU6MUU55TKVBFQMSM62C3TMMWU/events.json","paper":"https://pith.science/paper/XU6MUU55"},"agent_actions":{"view_html":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU","download_json":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU.json","view_paper":"https://pith.science/paper/XU6MUU55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.0626&json=true","fetch_graph":"https://pith.science/api/pith-number/XU6MUU55TKVBFQMSM62C3TMMWU/graph.json","fetch_events":"https://pith.science/api/pith-number/XU6MUU55TKVBFQMSM62C3TMMWU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU/action/storage_attestation","attest_author":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU/action/author_attestation","sign_citation":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU/action/citation_signature","submit_replication":"https://pith.science/pith/XU6MUU55TKVBFQMSM62C3TMMWU/action/replication_record"}},"created_at":"2026-05-18T04:33:18.291231+00:00","updated_at":"2026-05-18T04:33:18.291231+00:00"}