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For every g=2^h+1>8, we construct a curve X attaining the Nakajima bound and determine its relevant properties: X is a bielliptic curve with r=g, and its K-automorphism group has a dihedral K-automorphism group of order 4(g-1) which fixes no point in X. Moreover, we provide a classification of 2-groups S of K-automorphisms not fixing a point of X and such that |S|> 2g-1."},"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":"1104.5159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-27T14:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"5aa5ecf6a76c0e1bc7dcc79d06777a909eec48e491f5828eb67f2bdc097535a3","abstract_canon_sha256":"753621d83e0e06823032ed58be3cc4e413c103ffca514df4d516d8f19ebbecf6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:22.500097Z","signature_b64":"DyWvzI/HLYm0UH7nlIzdLnsor3d15VLr77uUTnivEa2Uoa4ciFQv5tA5kiFF3yqJNwyuAy4ZHm/0r3o8YVm1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c75fa3d63b0fade4810cc46ad01510d133296a478cad0c8fd92aa4ad7188642","last_reissued_at":"2026-05-18T04:23:22.499523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:22.499523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large 2-groups of automorphisms of curves with positive 2-rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gabor Korchmaros, Massimo Giulietti","submitted_at":"2011-04-27T14:57:43Z","abstract_excerpt":"Let K be an algebraically closed field of characteristic 2, and let X be a curve over K of genus g>1 and 2-rank r>0. 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