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This allows us to give a complete criterion in the case where q=p is a prime number. In particular, we show the following result: If X is a smooth hypersurface of dimension n and degree d admitting an automorphism of prime order p then p<(d-1)^{n+1}; and if p>(d-1)^n then X is isomorphic to the Klein hypersurface, n=2 or n+2 is prime, and p=\\Phi_{n+2}(1-d) where \\Phi_{"},"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":"1102.3443","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-16T22:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"22e217196228e7d55e7d5959468521ce6fce5ee9b0eadce395781c33531bd0c2","abstract_canon_sha256":"c5c7f95a07e0ccc9ec834e3982208b691e5f00d1fb3252a9f072f66153b8e4c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:42.641892Z","signature_b64":"HCQEOKy0MRtHN9PTZ56C+N8n26BLId3NvWkN0YMLd88AxiZSFDiMwU+cMy6vFjxQ5veKIi0Iu7ynP/H61u3MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff6f270922fa18e16b4935a3f45bc15568f9f45c2f6ba38e3505d0767b057330","last_reissued_at":"2026-05-18T02:56:42.641481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:42.641481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the order of an automorphism of a smooth hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alvaro Liendo, V\\'ictor Gonz\\'alez-Aguilera","submitted_at":"2011-02-16T22:12:39Z","abstract_excerpt":"In this paper we give an effective criterion as to when a positive integer q is the order of an automorphism of a smooth hypersurface of dimension n and degree d, for every d>2, n>1, (n,d)\\neq (2,4), and \\gcd(q,d)=\\gcd(q,d-1)=1. This allows us to give a complete criterion in the case where q=p is a prime number. In particular, we show the following result: If X is a smooth hypersurface of dimension n and degree d admitting an automorphism of prime order p then p<(d-1)^{n+1}; and if p>(d-1)^n then X is isomorphic to the Klein hypersurface, n=2 or n+2 is prime, and p=\\Phi_{n+2}(1-d) where \\Phi_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3443","kind":"arxiv","version":3},"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":"1102.3443","created_at":"2026-05-18T02:56:42.641544+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.3443v3","created_at":"2026-05-18T02:56:42.641544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3443","created_at":"2026-05-18T02:56:42.641544+00:00"},{"alias_kind":"pith_short_12","alias_value":"75XSOCJC7IMO","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"75XSOCJC7IMOC22J","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"75XSOCJC","created_at":"2026-05-18T12:26:22.705136+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/75XSOCJC7IMOC22JGWR7IW6BKV","json":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV.json","graph_json":"https://pith.science/api/pith-number/75XSOCJC7IMOC22JGWR7IW6BKV/graph.json","events_json":"https://pith.science/api/pith-number/75XSOCJC7IMOC22JGWR7IW6BKV/events.json","paper":"https://pith.science/paper/75XSOCJC"},"agent_actions":{"view_html":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV","download_json":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV.json","view_paper":"https://pith.science/paper/75XSOCJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.3443&json=true","fetch_graph":"https://pith.science/api/pith-number/75XSOCJC7IMOC22JGWR7IW6BKV/graph.json","fetch_events":"https://pith.science/api/pith-number/75XSOCJC7IMOC22JGWR7IW6BKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV/action/storage_attestation","attest_author":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV/action/author_attestation","sign_citation":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV/action/citation_signature","submit_replication":"https://pith.science/pith/75XSOCJC7IMOC22JGWR7IW6BKV/action/replication_record"}},"created_at":"2026-05-18T02:56:42.641544+00:00","updated_at":"2026-05-18T02:56:42.641544+00:00"}