{"id":"https://openalex.org/W7214009223","doi":"https://doi.org/10.48550/arxiv.2609.22557","title":"Maximal singular curves over finite fields from elliptic and hyperelliptic curves","display_name":"Maximal singular curves over finite fields from elliptic and hyperelliptic curves","publication_year":2026,"publication_date":"2026-09-18","ids":{"openalex":"https://openalex.org/W7214009223","doi":"https://doi.org/10.48550/arxiv.2609.22557"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.22557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22557","pdf_url":"https://arxiv.org/pdf/2609.22557","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.22557","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075593264","display_name":"Cesar Hilario","orcid":"https://orcid.org/0009-0005-8076-7985","observed_orcids":["https://orcid.org/0009-0005-8076-7985"]},"institutions":[{"id":"https://openalex.org/I65285256","display_name":"Pontificia Universidad Cat\u00f3lica del Per\u00fa","ror":"https://ror.org/00013q465","country_code":"PE","type":"education","lineage":["https://openalex.org/I65285256"]}],"countries":["PE"],"is_corresponding":false,"raw_author_name":"Hilario, Cesar","raw_affiliation_strings":["Departamento de Ciencias , Pontificia Universidad Cat\u00f3lica del Per\u00fa , Av. Universitaria 1801 , San Miguel 15088 , Lima , Peru"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Ciencias , Pontificia Universidad Cat\u00f3lica del Per\u00fa , Av. Universitaria 1801 , San Miguel 15088 , Lima , Peru","institution_ids":["https://openalex.org/I65285256"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116082847","display_name":"Rodrigo Salom\u00e3o","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Salom\u00e3o, Rodrigo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079441651","display_name":"Renato Vidal Martins","orcid":"https://orcid.org/0009-0000-2723-4200","observed_orcids":["https://orcid.org/0009-0000-2723-4200"]},"institutions":[{"id":"https://openalex.org/I65285256","display_name":"Pontificia Universidad Cat\u00f3lica del Per\u00fa","ror":"https://ror.org/00013q465","country_code":"PE","type":"education","lineage":["https://openalex.org/I65285256"]}],"countries":["PE"],"is_corresponding":false,"raw_author_name":"Martins, Renato Vidal","raw_affiliation_strings":["Departamento de Ciencias , Pontificia Universidad Cat\u00f3lica del Per\u00fa , Av. Universitaria 1801 , San Miguel 15088 , Lima , Peru"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Ciencias , Pontificia Universidad Cat\u00f3lica del Per\u00fa , Av. Universitaria 1801 , San Miguel 15088 , Lima , Peru","institution_ids":["https://openalex.org/I65285256"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.8989999890327454},{"id":"https://openalex.org/keywords/elliptic-curves","display_name":"elliptic curves","score":0.8349999785423279},{"id":"https://openalex.org/keywords/hyperelliptic-curves","display_name":"hyperelliptic curves","score":1.0},{"id":"https://openalex.org/keywords/rational-points","display_name":"rational points","score":0.6520000100135803},{"id":"https://openalex.org/keywords/cusps","display_name":"cusps","score":0.9890000224113464},{"id":"https://openalex.org/keywords/linear-projection","display_name":"linear projection","score":0.7620000243186951},{"id":"https://openalex.org/keywords/geometric-embedding","display_name":"geometric embedding","score":0.7139999866485596},{"id":"https://openalex.org/keywords/gorenstein-curves","display_name":"Gorenstein curves","score":0.8870000243186951},{"id":"https://openalex.org/keywords/trigonal-curves","display_name":"trigonal curves","score":0.9049999713897705},{"id":"https://openalex.org/keywords/gonality","display_name":"gonality","score":0.7160000205039978}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8392999768257141},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6169999837875366},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.5385000109672546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5216000080108643},{"id":"https://openalex.org/C79993320","wikidata":"https://www.wikidata.org/wiki/Q6119657","display_name":"Jacobian curve","level":5,"score":0.5195000171661377},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.48350000381469727},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.46050000190734863},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.41029998660087585},{"id":"https://openalex.org/C12516240","wikidata":"https://www.wikidata.org/wiki/Q5641621","display_name":"Half-period ratio","level":5,"score":0.3935000002384186},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.3921999931335449},{"id":"https://openalex.org/C131182338","wikidata":"https://www.wikidata.org/wiki/Q7858596","display_name":"Twists of curves","level":5,"score":0.3732999861240387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36890000104904175},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.36500000953674316},{"id":"https://openalex.org/C11074058","wikidata":"https://www.wikidata.org/wiki/Q850110","display_name":"Hyperelliptic curve","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C87905105","wikidata":"https://www.wikidata.org/wiki/Q5284582","display_name":"Division polynomials","level":5,"score":0.32330000400543213},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C166780011","wikidata":"https://www.wikidata.org/wiki/Q3005926","display_name":"Hyperelliptic curve cryptography","level":5,"score":0.28459998965263367},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C184363387","wikidata":"https://www.wikidata.org/wiki/Q3001219","display_name":"Stable curve","level":4,"score":0.26159998774528503},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.25940001010894775}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.22557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22557","pdf_url":"https://arxiv.org/pdf/2609.22557","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.22557","doi":"https://doi.org/10.48550/arxiv.2609.22557","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.22557","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.22557","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22557","pdf_url":"https://arxiv.org/pdf/2609.22557","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214009223.pdf","grobid_xml":"https://content.openalex.org/works/W7214009223.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W43450662","https://openalex.org/W2949212695","https://openalex.org/W2154728822","https://openalex.org/W1619997617","https://openalex.org/W7067284624","https://openalex.org/W7099538823","https://openalex.org/W2084688144","https://openalex.org/W21634141","https://openalex.org/W4417166487","https://openalex.org/W7039747315"],"abstract_inverted_index":{"We":[0],"construct":[1],"explicit":[2],"families":[3],"of":[4,28,36,77,85,93,115],"maximal":[5,12,107],"singular":[6,13,62],"curves":[7,63,88],"over":[8,43,56],"finite":[9,45],"fields.":[10],"A":[11],"curve":[14,17,42,54],"is":[15,24,99],"a":[16,40,44,49],"that":[18],"attains":[19],"the":[20,25,29,33,90,102,113],"Aubry-Perret":[21],"bound,":[22],"which":[23],"natural":[26],"extension":[27],"Hasse-Weil-Serre":[30],"bound":[31],"on":[32,39],"maximum":[34],"number":[35],"rational":[37],"points":[38],"smooth":[41,50,106],"field.":[46],"Starting":[47],"from":[48],"elliptic":[51],"or":[52,68],"hyperelliptic":[53,86],"$\\tilde{C}$":[55],"$\\mathbb{F}_{q}$":[57],"($q$":[58],"odd),":[59],"we":[60,73,81,110],"generate":[61],"$C$":[64],"with":[65],"non-split":[66],"nodes":[67],"cusps.":[69],"In":[70],"our":[71],"approach":[72],"use":[74],"linear":[75],"projections":[76],"geometric":[78],"embeddings,":[79],"and":[80,89,104],"apply":[82],"St\u00f6hr's":[83],"embedding":[84],"Gorenstein":[87,95],"Rosa-St\u00f6hr":[91],"theory":[92],"trigonal":[94],"curves.":[96,108,118],"The":[97],"construction":[98],"applied":[100],"to":[101],"Tafazolian":[103],"Tafazolian-Torres":[105],"Finally,":[109],"also":[111],"determine":[112],"gonality":[114],"all":[116],"obtained":[117]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-23T00:00:00"}