{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PXZRXAOBMZ5VYJJZ7T5DKSA2SH","short_pith_number":"pith:PXZRXAOB","schema_version":"1.0","canonical_sha256":"7df31b81c1667b5c2539fcfa35481a91f932b730f9749cd1438ab4dd0f1d4ade","source":{"kind":"arxiv","id":"1611.00875","version":2},"attestation_state":"computed","paper":{"title":"The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fei Hu","submitted_at":"2016-11-03T03:56:09Z","abstract_excerpt":"Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\\mathrm{Aut}(X,D)$. We show that $G$ is a semi-abelian variety of dimension $\\le \\min\\{n-\\bar{\\kappa}(V), n\\}$ with $V := X\\setminus D$. In the dimension two, Shigeru Iitaka claimed in his 1979 Osaka J. Math. paper that $\\dim G\\le \\bar{q}(V)$ for a log smooth surface pair with $\\bar{\\kappa}(V) = 0$ and $\\bar{p}_g(V) = 1$. We (re)prove and generalize this classical result for all surfaces with"},"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":"1611.00875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-03T03:56:09Z","cross_cats_sorted":[],"title_canon_sha256":"dcddde9307cd16d0393ca624144abe942ccbc287f637e4c978e5943865008480","abstract_canon_sha256":"580e503cbf884dd3e1b47bfba57bbdc26a7efa2c07e69dfa6e0b971bf3842ba8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:28.012462Z","signature_b64":"WUspsN9xVmPcVF0M5B0lRwmoDaK+k6TZillICxDI1DyVwtAE+BQ1QKjxlJBGZGAGKuP+bIbaXfmH7dP9r4jPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7df31b81c1667b5c2539fcfa35481a91f932b730f9749cd1438ab4dd0f1d4ade","last_reissued_at":"2026-05-17T23:41:28.011763Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:28.011763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fei Hu","submitted_at":"2016-11-03T03:56:09Z","abstract_excerpt":"Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\\mathrm{Aut}(X,D)$. We show that $G$ is a semi-abelian variety of dimension $\\le \\min\\{n-\\bar{\\kappa}(V), n\\}$ with $V := X\\setminus D$. In the dimension two, Shigeru Iitaka claimed in his 1979 Osaka J. Math. paper that $\\dim G\\le \\bar{q}(V)$ for a log smooth surface pair with $\\bar{\\kappa}(V) = 0$ and $\\bar{p}_g(V) = 1$. We (re)prove and generalize this classical result for all surfaces with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00875","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":"1611.00875","created_at":"2026-05-17T23:41:28.011875+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.00875v2","created_at":"2026-05-17T23:41:28.011875+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00875","created_at":"2026-05-17T23:41:28.011875+00:00"},{"alias_kind":"pith_short_12","alias_value":"PXZRXAOBMZ5V","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PXZRXAOBMZ5VYJJZ","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PXZRXAOB","created_at":"2026-05-18T12:30:39.010887+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/PXZRXAOBMZ5VYJJZ7T5DKSA2SH","json":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH.json","graph_json":"https://pith.science/api/pith-number/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/graph.json","events_json":"https://pith.science/api/pith-number/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/events.json","paper":"https://pith.science/paper/PXZRXAOB"},"agent_actions":{"view_html":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH","download_json":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH.json","view_paper":"https://pith.science/paper/PXZRXAOB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.00875&json=true","fetch_graph":"https://pith.science/api/pith-number/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/graph.json","fetch_events":"https://pith.science/api/pith-number/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/action/storage_attestation","attest_author":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/action/author_attestation","sign_citation":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/action/citation_signature","submit_replication":"https://pith.science/pith/PXZRXAOBMZ5VYJJZ7T5DKSA2SH/action/replication_record"}},"created_at":"2026-05-17T23:41:28.011875+00:00","updated_at":"2026-05-17T23:41:28.011875+00:00"}