{"id":"https://openalex.org/W2763390622","doi":"https://doi.org/10.1080/10586458.2009.10129059","title":"Rationality of Moduli Spaces of Plane Curves of Small Degree","display_name":"Rationality of Moduli Spaces of Plane Curves of Small Degree","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2763390622","doi":"https://doi.org/10.1080/10586458.2009.10129059","mag":"2763390622"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2009.10129059","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2009.10129059","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012833892","display_name":"Christian B\u00f6hning","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian B\u00f6hning","raw_affiliation_strings":["Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universit\u00e4t G\u00f6ttingen, Bunsenstr. 3\u20135, G\u00f6ttingen, 37073, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universit\u00e4t G\u00f6ttingen, Bunsenstr. 3\u20135, G\u00f6ttingen, 37073, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051323797","display_name":"Hans\u2010Christian Graf von Bothmer","orcid":"https://orcid.org/0000-0003-0136-444X"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans-Christian Graf von Bothmer","raw_affiliation_strings":["Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universit\u00e4t G\u00f6ttingen, Bunsenstr. 3\u20135, G\u00f6ttingen, 37073, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universit\u00e4t G\u00f6ttingen, Bunsenstr. 3\u20135, G\u00f6ttingen, 37073, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061022616","display_name":"Jakob Kr\u00f6ker","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jakob Kr\u00f6ker","raw_affiliation_strings":["Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universit\u00e4t G\u00f6ttingen, Bunsenstr. 3\u20135, G\u00f6ttingen, 37073, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Courant Research Center for Higher Order Structures, Georg-August-Universit\u00e4t G\u00f6ttingen, Bunsenstr. 3\u20135, G\u00f6ttingen, 37073, Germany","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012833892"],"corresponding_institution_ids":["https://openalex.org/I74656192"],"apc_list":null,"apc_paid":null,"fwci":0.3856,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.63913277,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"18","issue":"4","first_page":"499","last_page":"508"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9894999861717224,"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":0.9894999861717224,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9129999876022339,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/mathematics","display_name":"Mathematics","score":0.8826571106910706},{"id":"https://openalex.org/keywords/moduli-space","display_name":"Moduli space","score":0.7951629161834717},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7601318359375},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.6996485590934753},{"id":"https://openalex.org/keywords/moduli-of-algebraic-curves","display_name":"Moduli of algebraic curves","score":0.5686457753181458},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5609564781188965},{"id":"https://openalex.org/keywords/modular-equation","display_name":"Modular equation","score":0.5548318028450012},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5242729187011719},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.5146297216415405},{"id":"https://openalex.org/keywords/projective-space","display_name":"Projective space","score":0.4834355115890503},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.47759032249450684},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4500739872455597},{"id":"https://openalex.org/keywords/rationality","display_name":"Rationality","score":0.4432031512260437},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44280922412872314},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26479092240333557},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.17426875233650208},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04738891124725342}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8826571106910706},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.7951629161834717},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7601318359375},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.6996485590934753},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.5686457753181458},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5609564781188965},{"id":"https://openalex.org/C55247095","wikidata":"https://www.wikidata.org/wiki/Q6889716","display_name":"Modular equation","level":4,"score":0.5548318028450012},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5242729187011719},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.5146297216415405},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.4834355115890503},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.47759032249450684},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4500739872455597},{"id":"https://openalex.org/C201717286","wikidata":"https://www.wikidata.org/wiki/Q938185","display_name":"Rationality","level":2,"score":0.4432031512260437},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44280922412872314},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26479092240333557},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.17426875233650208},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04738891124725342},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2009.10129059","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2009.10129059","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1259158510","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1259158510","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.316.291","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.316.291","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0904.0890v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1997663493","https://openalex.org/W2034756523","https://openalex.org/W2046387829","https://openalex.org/W2073752877","https://openalex.org/W2129690011","https://openalex.org/W2313315128","https://openalex.org/W2794078600","https://openalex.org/W2911828567"],"related_works":["https://openalex.org/W2942869015","https://openalex.org/W1978908735","https://openalex.org/W3113721622","https://openalex.org/W78148973","https://openalex.org/W1496979297","https://openalex.org/W3190357833","https://openalex.org/W4313240746","https://openalex.org/W4301784168","https://openalex.org/W2024972907","https://openalex.org/W2950606863"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"the":[3],"moduli":[4],"space":[5],"C(d)":[6],"of":[7,10],"plane":[8],"curves":[9],"degree":[11],"d":[12,23],"(with":[13],"respect":[14],"to":[15],"projective":[16],"equivalence)":[17],"is":[18],"rational":[19],"except":[20],"possibly":[21],"if":[22],"=":[24],"6,":[25],"7,":[26],"8,":[27],"11,":[28],"12,":[29],"14,":[30],"15,":[31],"16,":[32],"18,":[33],"20,":[34],"23,":[35],"24,":[36],"26,":[37],"32,":[38],"48.":[39]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}