{"id":"https://openalex.org/W7208838821","doi":"https://doi.org/10.48550/arxiv.2609.03976","title":"A Polynomial PDE Criterion for the $-n/d$ Root of the Bernstein-Sato polynomial of Homogeneous Ideals","display_name":"A Polynomial PDE Criterion for the $-n/d$ Root of the Bernstein-Sato polynomial of Homogeneous Ideals","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7208838821","doi":"https://doi.org/10.48550/arxiv.2609.03976"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.03976","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03976","pdf_url":"https://arxiv.org/pdf/2609.03976","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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/2609.03976","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150281194","display_name":"Yifan Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Yifan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055015678","display_name":"Huaiqing Zuo","orcid":"https://orcid.org/0000-0003-0865-6605","observed_orcids":["https://orcid.org/0000-0003-0865-6605"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuo, Huaiqing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.7128999829292297,"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":0.7128999829292297,"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":0.24770000576972961,"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":0.013100000098347664,"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/bernstein-sato-polynomial","display_name":"Bernstein-Sato polynomial","score":1.0},{"id":"https://openalex.org/keywords/homogeneous-ideals","display_name":"homogeneous ideals","score":0.8230000138282776},{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.8180000185966492},{"id":"https://openalex.org/keywords/monodromy-conjecture","display_name":"monodromy conjecture","score":0.9229999780654907},{"id":"https://openalex.org/keywords/maximal-minors","display_name":"maximal minors","score":0.7160000205039978},{"id":"https://openalex.org/keywords/determinantal-ideals","display_name":"determinantal ideals","score":0.7760000228881836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.888700008392334},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.6823999881744385},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5817999839782715},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5181000232696533},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.5142999887466431},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.48069998621940613},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4560000002384186},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4521999955177307},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.4456999897956848},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C107775665","wikidata":"https://www.wikidata.org/wiki/Q12859399","display_name":"Properties of polynomial roots","level":4,"score":0.4041999876499176},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4027999937534332},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.4016000032424927},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3767000138759613},{"id":"https://openalex.org/C1366977","wikidata":"https://www.wikidata.org/wiki/Q2621270","display_name":"Routh\u2013Hurwitz stability criterion","level":3,"score":0.34599998593330383},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.33970001339912415},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.3278000056743622},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.3212999999523163},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.30140000581741333},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.25769999623298645},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.03976","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03976","pdf_url":"https://arxiv.org/pdf/2609.03976","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.03976","doi":"https://doi.org/10.48550/arxiv.2609.03976","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.03976","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.03976","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03976","pdf_url":"https://arxiv.org/pdf/2609.03976","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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/W7208838821.pdf","grobid_xml":"https://content.openalex.org/works/W7208838821.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4404345900","https://openalex.org/W4406272996","https://openalex.org/W7162432050","https://openalex.org/W7204492855"],"related_works":["https://openalex.org/W7221765668","https://openalex.org/W7221036081","https://openalex.org/W4302554739","https://openalex.org/W2966692121","https://openalex.org/W2029479765","https://openalex.org/W2948222788","https://openalex.org/W6964327346","https://openalex.org/W1982063110","https://openalex.org/W7168515816","https://openalex.org/W7131413230"],"abstract_inverted_index":{"Let":[0],"$I\\subseteq\\mathbb":[1],"C[x_1,\\ldots,x_n]$":[2],"be":[3,124],"an":[4],"ideal":[5,40],"generated":[6],"by":[7],"homogeneous":[8,113],"polynomials":[9,116],"of":[10,29,41,44,89,112],"a":[11,17,27,45],"common":[12],"degree":[13],"$d$.":[14],"We":[15,34],"give":[16],"polynomial":[18,32],"partial":[19],"differential":[20],"equation":[21],"criterion":[22,37,81],"guaranteeing":[23],"that":[24,79],"$-n/d$":[25],"is":[26,82],"root":[28,54,122],"the":[30,39,52,68,73,80,86,90,99,119],"Bernstein-Sato":[31,121,127],"$b_I(s)$.":[33],"apply":[35],"this":[36,63],"to":[38,66],"maximal":[42],"minors":[43],"generic":[46],"$m\\times":[47],"n$":[48],"matrix":[49],"and":[50,103,115],"obtain":[51,67],"distinguished":[53,120],"$-n$;":[55],"combined":[56],"with":[57],"local":[58],"divisibility":[59],"along":[60],"determinantal":[61],"strata,":[62],"allows":[64],"us":[65],"strong":[69],"monodromy":[70,129],"conjecture":[71],"in":[72,94],"maximal-minor":[74],"case.":[75],"Finally,":[76],"we":[77],"prove":[78],"stable":[83],"under":[84],"enlarging":[85],"linear":[87],"span":[88],"generators,":[91],"adjoining":[92],"generators":[93],"disjoint":[95],"variables,":[96],"products":[97],"satisfying":[98],"natural":[100],"slope":[101],"condition,":[102],"Thom-Sebastiani":[104],"sums.":[105],"These":[106],"stability":[107],"results":[108],"provide":[109],"new":[110],"classes":[111],"ideals":[114],"for":[117],"which":[118],"can":[123],"detected.":[125],"Keywords.":[126],"polynomial,":[128],"conjecture.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-06T00:00:00"}
