{"id":"https://openalex.org/W7213612886","doi":"https://doi.org/10.48550/arxiv.2609.19869","title":"Bounds for Codimension-One Components of Zero Loci of Bernstein-Sato Ideals","display_name":"Bounds for Codimension-One Components of Zero Loci of Bernstein-Sato Ideals","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213612886","doi":"https://doi.org/10.48550/arxiv.2609.19869"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19869","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19869","pdf_url":"https://arxiv.org/pdf/2609.19869","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/2609.19869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152150110","display_name":"Wenzong Guo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Wenzong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5152113633","display_name":"Fanghan Xiang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiang, Fanghan","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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.8256999850273132,"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":0.8256999850273132,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.15530000627040863,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/bernstein-sato-polynomial","display_name":"Bernstein-Sato polynomial","score":0.8330000042915344},{"id":"https://openalex.org/keywords/zero-loci","display_name":"zero loci","score":0.8619999885559082},{"id":"https://openalex.org/keywords/log-resolution","display_name":"log resolution","score":0.5529999732971191}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9204999804496765},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.6581000089645386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6248999834060669},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6115999817848206},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5437999963760376},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4875999987125397},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4578999876976013},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4320000112056732},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4318000078201294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41100001335144043},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3864000141620636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3411000072956085},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C17327563","wikidata":"https://www.wikidata.org/wiki/Q1991405","display_name":"Nowhere dense set","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.29820001125335693},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.2897000014781952},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.27970001101493835},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C119322782","wikidata":"https://www.wikidata.org/wiki/Q2662236","display_name":"VC dimension","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.25130000710487366},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19869","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19869","pdf_url":"https://arxiv.org/pdf/2609.19869","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.2609.19869","doi":"https://doi.org/10.48550/arxiv.2609.19869","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19869","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:2609.19869","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19869","pdf_url":"https://arxiv.org/pdf/2609.19869","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/W7213612886.pdf","grobid_xml":"https://content.openalex.org/works/W7213612886.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3133450139","https://openalex.org/W7167735287"],"related_works":["https://openalex.org/W3211638551","https://openalex.org/W7220671877","https://openalex.org/W3049457854","https://openalex.org/W4288798080","https://openalex.org/W4402701398","https://openalex.org/W6964327346","https://openalex.org/W6891803294","https://openalex.org/W4413339252","https://openalex.org/W2952591146","https://openalex.org/W7214707380"],"abstract_inverted_index":{"Let":[0],"$X$":[1,22],"be":[2,14],"a":[3,15,48,60,69,74,197],"smooth":[4],"complex":[5],"affine":[6],"variety":[7],"of":[8,17,35,56,62,77,86,105,109,148,155,200,208],"dimension":[9],"$n$,":[10],"and":[11,83,99,129,132,166,178,215],"let":[12],"$F=(f_1,\\ldots,f_r)$":[13],"tuple":[16],"nonzero":[18],"regular":[19],"functions":[20,214],"on":[21],"such":[23,111],"that":[24,92,171],"$f:=\\prod_{i=1}^r":[25],"f_i$":[26],"is":[27,59,101],"not":[28],"invertible.":[29],"We":[30,72,89,194],"study":[31],"the":[32,36,63,102,133,140,145,152,167,175,191,201,206,216],"zero":[33],"loci":[34],"Bernstein-Sato":[37],"ideals":[38],"$B_F^{\\mathbf":[39],"a}$":[40],"for":[41,115,120],"nonnegative":[42],"integral":[43],"shifts":[44],"$\\mathbf":[45],"a$.":[46],"For":[47],"fixed":[49],"log":[50],"resolution,":[51],"every":[52],"codimension-one":[53],"irreducible":[54],"component":[55],"$Z(B_F^{\\mathbf":[57,149],"a})$":[58],"hyperplane":[61],"form":[64],"$L_E(\\mathbf":[65],"s)+k_E+c=0$":[66],"with":[67,151,163],"$c$":[68],"positive":[70],"integer.":[71],"give":[73],"new":[75],"proof":[76],"this":[78],"result":[79],"using":[80],"localized":[81],"maximal":[82],"minimal":[84,103],"extensions":[85],"relative":[87],"D-modules.":[88],"also":[90],"prove":[91],"$c\\leq":[93],"L_E(\\mathbf":[94],"a)+(n-1-\u03b4_f)L_E(\\mathbf":[95],"1)-k_E$,":[96],"where":[97],"$\u03b4_f=\\min\\{n-1,\u03b1_f\\}$":[98],"$\u03b1_f$":[100],"exponent":[104],"$f$.":[106],"The":[107],"problem":[108],"obtaining":[110],"an":[112],"upper":[113,141,192],"bound":[114],"arbitrary":[116],"tuples":[117],"(in":[118],"particular,":[119],"$r>1$)":[121],"was":[122],"raised":[123],"by":[124,160],"Budur,":[125],"van":[126],"der":[127],"Veer,":[128],"Van":[130],"Werde,":[131],"above":[134],"inequality":[135],"resolves":[136],"it.":[137],"To":[138],"obtain":[139],"bound,":[142],"we":[143],"compare":[144],"diagonal":[146,164],"slice":[147],"1})$":[150],"root":[153,182],"set":[154],"$b_f$.":[156],"A":[157],"finite":[158],"covering":[159],"translates,":[161],"combined":[162],"specialization":[165],"log-resolution":[168],"description,":[169],"shows":[170],"these":[172],"sets":[173],"have":[174],"same":[176],"least":[177,187],"greatest":[179],"points.":[180],"Saito's":[181],"estimate":[183],"at":[184],"their":[185],"common":[186],"point":[188],"then":[189],"yields":[190],"bound.":[193],"further":[195],"establish":[196],"divisor-valued":[198],"formulation":[199],"local":[202],"index":[203],"comparison,":[204],"recovering":[205],"detection":[207],"monodromy":[209,212],"support":[210],"via":[211],"zeta":[213],"multivariable":[217],"A'Campo":[218],"formula.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}