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If the grading on the algebra of regular functions $\\mathbb{K}[X]$ defined by the action of $\\mathbb{T}$ is pointed, the group $\\text{Aut}(X)$ is a finite extension of $\\mathbb{T}$. As an application, we describe the automorphism group of a rigid trinomial affine hypersurface and find all isomorphisms between such hypersurfaces."},"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":"1607.03472","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-12T19:34:35Z","cross_cats_sorted":[],"title_canon_sha256":"9f45123af76624439ae7360b9a1e4d3bd5244326ebbcd3424793aeb28270ff81","abstract_canon_sha256":"110d7ae081e0c1911964b6d050293e49ababd615943da865fd1c901100cbc11d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:20.888452Z","signature_b64":"5Hg5frE80ZaCk5BIAPREsGNo6EnoLwSsRmiNIuIAhG9QmaQmuCs4RGs9odcX+7SiUp+/Vr62Bp1uMxgxQsaGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93510142ab6c330869623d6a396d45b69379757d6ccc01bdafc3c18495e1cce7","last_reissued_at":"2026-05-18T00:46:20.888077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:20.888077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The automorphism group of a rigid affine variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Arzhantsev, Sergey Gaifullin","submitted_at":"2016-07-12T19:34:35Z","abstract_excerpt":"An irreducible algebraic variety $X$ is rigid if it admits no nontrivial action of the additive group of the ground field. 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