{"id":"https://openalex.org/W7212913416","doi":"https://doi.org/10.48550/arxiv.2609.12253","title":"Numerical invariants for three-generated ideals","display_name":"Numerical invariants for three-generated ideals","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212913416","doi":"https://doi.org/10.48550/arxiv.2609.12253"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12253","pdf_url":"https://arxiv.org/pdf/2609.12253","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/2609.12253","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069991409","display_name":"Marcos Jardim","orcid":"https://orcid.org/0000-0002-8419-7044","observed_orcids":["https://orcid.org/0000-0002-8419-7044"]},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jardim, Marcos","raw_affiliation_strings":["Universidade Estadual de Campinas (UNICAMP) , Instituto de Matem\u00e1tica , Estat\u00edstica e Computac \u00b8\u00e3o Cient\u00edfica (IMECC) , Departamento de Matem\u00e1tica , Rua S\u00e9rgio Buarque de Holanda , 651 , 13083-970 Campinas-SP , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Estadual de Campinas (UNICAMP) , Instituto de Matem\u00e1tica , Estat\u00edstica e Computac \u00b8\u00e3o Cient\u00edfica (IMECC) , Departamento de Matem\u00e1tica , Rua S\u00e9rgio Buarque de Holanda , 651 , 13083-970 Campinas-SP , Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133147163","display_name":"Felipe Monteiro","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Monteiro, Felipe","raw_affiliation_strings":["Universidade Estadual de Campinas (UNICAMP) , Instituto de Matem\u00e1tica , Estat\u00edstica e Computac \u00b8\u00e3o Cient\u00edfica (IMECC) , Departamento de Matem\u00e1tica , Rua S\u00e9rgio Buarque de Holanda , 651 , 13083-970 Campinas-SP , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Estadual de Campinas (UNICAMP) , Instituto de Matem\u00e1tica , Estat\u00edstica e Computac \u00b8\u00e3o Cient\u00edfica (IMECC) , Departamento de Matem\u00e1tica , Rua S\u00e9rgio Buarque de Holanda , 651 , 13083-970 Campinas-SP , Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066627498","display_name":"Abbas Nasrollah Nejad","orcid":"https://orcid.org/0000-0003-0511-6099","observed_orcids":["https://orcid.org/0000-0003-0511-6099"]},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Nejad, Abbas Nasrollah","raw_affiliation_strings":["Universidade Estadual de Campinas (UNICAMP) , Instituto de Matem\u00e1tica , Estat\u00edstica e Computac \u00b8\u00e3o Cient\u00edfica (IMECC) , Departamento de Matem\u00e1tica , Rua S\u00e9rgio Buarque de Holanda , 651 , 13083-970 Campinas-SP , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Estadual de Campinas (UNICAMP) , Instituto de Matem\u00e1tica , Estat\u00edstica e Computac \u00b8\u00e3o Cient\u00edfica (IMECC) , Departamento de Matem\u00e1tica , Rua S\u00e9rgio Buarque de Holanda , 651 , 13083-970 Campinas-SP , Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019956028","display_name":"Zaqueu Ramos","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ramos, Zaqueu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"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":2,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.006200000178068876,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.00039999998989515007,"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/plane-curves","display_name":"plane curves","score":0.8199999928474426},{"id":"https://openalex.org/keywords/realizability","display_name":"realizability","score":0.7739999890327454},{"id":"https://openalex.org/keywords/minimal-graded-free-resolutions","display_name":"minimal graded free resolutions","score":0.9200000166893005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8406999707221985},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.5776000022888184},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5436999797821045},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.5400999784469604},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.4510999917984009},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4503999948501587},{"id":"https://openalex.org/C55101346","wikidata":"https://www.wikidata.org/wiki/Q85776755","display_name":"Hilbert's syzygy theorem","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41819998621940613},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4027000069618225},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C143904861","wikidata":"https://www.wikidata.org/wiki/Q2297037","display_name":"Isolated singularity","level":3,"score":0.30070000886917114},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.2619999945163727}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12253","pdf_url":"https://arxiv.org/pdf/2609.12253","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.2609.12253","doi":"https://doi.org/10.48550/arxiv.2609.12253","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12253","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12253","pdf_url":"https://arxiv.org/pdf/2609.12253","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":[{"id":"https://openalex.org/G1811992940","display_name":null,"funder_award_id":"305601/2022-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3525068622","display_name":"Brazilian Center for Geometry (CBG)","funder_award_id":"24/00923-6","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G6438247056","display_name":null,"funder_award_id":"2021/","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G6756993358","display_name":null,"funder_award_id":"/2022-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323854","display_name":"Universidade Estadual de Campinas","ror":"https://ror.org/04wffgt70"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212913416.pdf","grobid_xml":"https://content.openalex.org/works/W7212913416.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7151341253"],"related_works":["https://openalex.org/W4402402735","https://openalex.org/W4386114286","https://openalex.org/W7213497050","https://openalex.org/W7160869638","https://openalex.org/W7151341253","https://openalex.org/W7123514309","https://openalex.org/W2577009157","https://openalex.org/W7214018029","https://openalex.org/W2998337052","https://openalex.org/W2087913446"],"abstract_inverted_index":{"We":[0,38,90],"study":[1,82],"numerical":[2,57,93],"invariants":[3],"of":[4,21,27,31,46,83,120,131],"homogeneous":[5,52],"ideals":[6,45,53],"generated":[7],"by":[8],"three":[9],"forms,":[10],"with":[11],"particular":[12],"emphasis":[13],"on":[14],"the":[15,18,22,25,28,32,35,40,61,64,68,74,81,106,116,135],"interaction":[16],"between":[17],"initial":[19],"degree":[20,42],"syzygy":[23],"module,":[24],"multiplicity":[26],"codimension-two":[29],"part":[30],"ideal,":[33],"and":[34,54,63,78,87,101,126],"Bourbaki":[36,41,118],"degree.":[37],"extend":[39,73],"from":[43,105],"gradient":[44],"plane":[47,124],"curves":[48,125],"to":[49,80],"arbitrary":[50],"three-generated":[51],"obtain":[55,102],"sharp":[56],"bounds":[58,72],"in":[59,97,129],"both":[60],"general":[62,98],"equigenerated":[65,69],"settings.":[66],"In":[67],"case,":[70],"these":[71],"du":[75],"Plessis--Wall":[76],"picture":[77],"lead":[79],"numerical,":[84],"structural,":[85],"dimensional,":[86],"integrable":[88],"gaps.":[89],"show":[91],"that":[92],"admissibility":[94],"does":[95],"not":[96],"imply":[99],"realizability":[100],"further":[103],"restrictions":[104],"minimal":[107],"graded":[108],"free":[109],"resolution.":[110],"As":[111],"an":[112],"application,":[113],"we":[114],"determine":[115],"possible":[117,136],"degrees":[119],"reduced":[121],"singular":[122],"quartic":[123],"describe":[127],"them":[128],"terms":[130],"their":[132],"singularity":[133],"configurations;":[134],"values":[137],"are":[138],"0,1,2,3,4,6,7,8.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}