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Let $Aut(\\mathcal{X})$ be the group of all automorphisms of $\\mathcal{X}$ which fix $\\mathbb{K}$ element-wise. For any solvable subgroup $G$ of $Aut(\\mathcal{X})$ we prove that $|G|\\leq 34 (\\mathcal{g}(\\mathcal{X})+1)^{3/2}$. There are known curves attaining this bound up to the constant $34$. For $p$ odd, our result improves the classical Nakajima bound $|G|\\leq 84(\\mat"},"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":"1610.05252","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-17T18:30:43Z","cross_cats_sorted":[],"title_canon_sha256":"dd753f2d9eed2ab805232af03eeef0895a32c64d4602d084d1f8bb6e5599fd52","abstract_canon_sha256":"0cabb78b7bc2dd05d648cf4e9752246a24d93e603273b751591fefcdb99d4d8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.655861Z","signature_b64":"Juu6yqz/LCrXBzDbJJJpKxrmtjDZ51lSM6v6+Hv0rTCeAS64155k9zL1sitMiOaIHptJdXFzl4WLLVkFmMxbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fb129124cea1de86b38352d0aa8a57bff1f64902f1ad3cba4b4e249c7481eef","last_reissued_at":"2026-05-17T23:52:08.655484Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.655484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ordinary algebraic curves with many automorphisms in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G\\'abor Korchm\\'aros, Maria Montanucci","submitted_at":"2016-10-17T18:30:43Z","abstract_excerpt":"Let $\\mathcal{X}$ be an ordinary (projective, geometrically irreducible, nonsingular) algebraic curve of genus $\\mathcal{g}(\\mathcal{X}) \\ge 2$ defined over an algebraically closed field $\\mathbb{K}$ of odd characteristic $p$. Let $Aut(\\mathcal{X})$ be the group of all automorphisms of $\\mathcal{X}$ which fix $\\mathbb{K}$ element-wise. For any solvable subgroup $G$ of $Aut(\\mathcal{X})$ we prove that $|G|\\leq 34 (\\mathcal{g}(\\mathcal{X})+1)^{3/2}$. There are known curves attaining this bound up to the constant $34$. 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