{"id":"https://openalex.org/W7221787780","doi":"https://doi.org/10.48550/arxiv.2610.16951","title":"Solomon--Terao Algebras: Top Degree, Dimension, and Homology","display_name":"Solomon--Terao Algebras: Top Degree, Dimension, and Homology","publication_year":2026,"publication_date":"2026-10-12","ids":{"openalex":"https://openalex.org/W7221787780","doi":"https://doi.org/10.48550/arxiv.2610.16951"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.16951","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16951","pdf_url":"https://arxiv.org/pdf/2610.16951","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/2610.16951","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158696106","display_name":"Hanyu Cai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cai, Hanyu","raw_affiliation_strings":["School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158747746","display_name":"Haiyang Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Haiyang","raw_affiliation_strings":["Qiuzhen College , Tsinghua University , Beijing 100084 , China","School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qiuzhen College , Tsinghua University , Beijing 100084 , China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153492094","display_name":"Shixuan Zeng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeng, Shixuan","raw_affiliation_strings":["School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108714746","display_name":"S Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Shanwei","raw_affiliation_strings":["School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of the Gifted Young , University of Science and Technology of China , No. 96 Jinzhai Road , Baohe District , Hefei , Anhui Province 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.7627000212669373,"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":0.7627000212669373,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.2045000046491623,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.011599999852478504,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/central-hyperplane-arrangements","display_name":"central hyperplane arrangements","score":0.9980000257492065},{"id":"https://openalex.org/keywords/orlik-solomon-algebra","display_name":"Orlik-Solomon algebra","score":0.9350000023841858},{"id":"https://openalex.org/keywords/homology-groups","display_name":"homology groups","score":0.6269999742507935},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.5770000219345093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8187999725341797},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.633899986743927},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.612500011920929},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6040999889373779},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.5569000244140625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5223000049591064},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4805999994277954},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4731999933719635},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43639999628067017},{"id":"https://openalex.org/C139962677","wikidata":"https://www.wikidata.org/wiki/Q1095056","display_name":"Singular homology","level":3,"score":0.3822000026702881},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38199999928474426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3813000023365021},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.3797999918460846},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34880000352859497},{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.16951","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16951","pdf_url":"https://arxiv.org/pdf/2610.16951","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.2610.16951","doi":"https://doi.org/10.48550/arxiv.2610.16951","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.16951","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:2610.16951","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16951","pdf_url":"https://arxiv.org/pdf/2610.16951","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":[{"id":"https://openalex.org/F4320314331","display_name":"Centre de Recherches Math\u00e9matiques","ror":"https://ror.org/03czdsq06"},{"id":"https://openalex.org/F4320324787","display_name":"Peking University","ror":"https://ror.org/02v51f717"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221787780.pdf","grobid_xml":"https://content.openalex.org/works/W7221787780.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4414594377"],"related_works":["https://openalex.org/W2963268090","https://openalex.org/W2599973460","https://openalex.org/W7098821961","https://openalex.org/W4385854333","https://openalex.org/W2165569759","https://openalex.org/W7098440059","https://openalex.org/W2950389628","https://openalex.org/W2081682255","https://openalex.org/W1967358891","https://openalex.org/W2795118461"],"abstract_inverted_index":{"We":[0,44],"study":[1],"the":[2,6,42,47,81,93,102,125],"Solomon--Terao":[3,7,48,126],"algebra":[4,49],"and":[5,57,74,117],"complex":[8,127],"of":[9,25,33,70,84,92,124],"a":[10,22,58,68],"central":[11],"hyperplane":[12],"arrangement":[13,103],"$\\mathcal":[14,34,104,112],"A$":[15,35,105,113],"in":[16],"$\\mathbb":[17],"C^\\ell$.":[18],"Let":[19],"$\u03b7$":[20,130],"be":[21],"homogeneous":[23],"polynomial":[24],"degree":[26,54],"$d\\geq2$":[27],"whose":[28],"restriction":[29],"to":[30],"every":[31],"flat":[32],"has":[36,52],"no":[37],"critical":[38],"point":[39],"away":[40],"from":[41],"origin.":[43],"prove":[45,110],"that":[46,80,91,101,111],"$\\mathrm{ST}(\\mathcal":[50,85],"A,\u03b7)$":[51,86],"top":[53,60],"$|\\mathcal":[55],"A|+\\ell(d-2)$":[56],"one-dimensional":[59],"graded":[61],"component":[62],"with":[63,129],"an":[64],"explicit":[65],"generator,":[66],"solving":[67],"conjecture":[69],"Abe,":[71],"Maeno,":[72],"Murai,":[73],"Numata.":[75],"For":[76],"$d=2$,":[77],"we":[78,109],"show":[79],"total":[82],"dimension":[83],"is":[87,106,114],"bounded":[88],"below":[89],"by":[90],"Orlik--Solomon":[94],"algebra.":[95],"Both":[96],"results":[97],"hold":[98],"without":[99],"assuming":[100],"tame.":[107],"Finally,":[108],"tame":[115],"if":[116,119],"only":[118],"all":[120],"positive-degree":[121],"homology":[122],"groups":[123],"associated":[128],"vanish.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}