{"id":"https://openalex.org/W7204790760","doi":"https://doi.org/10.48550/arxiv.2608.28372","title":"Local inequalities for $cD$ and $cE$ singularities","display_name":"Local inequalities for $cD$ and $cE$ singularities","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204790760","doi":"https://doi.org/10.48550/arxiv.2608.28372"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28372","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28372","pdf_url":"https://arxiv.org/pdf/2608.28372","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","license_id":"https://openalex.org/licenses/cc-by","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/2608.28372","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074371324","display_name":"Chi-Kang Chang","orcid":"https://orcid.org/0000-0002-5175-5847","observed_orcids":["https://orcid.org/0000-0002-5175-5847"]},"institutions":[{"id":"https://openalex.org/I4405259317","display_name":"RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences","ror":"https://ror.org/022hvg611","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4405259317"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Chang, Chi-Kang","raw_affiliation_strings":["RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) , 2-1 Hirosawa , Wako , Saitama 351-0198 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) , 2-1 Hirosawa , Wako , Saitama 351-0198 , Japan","institution_ids":["https://openalex.org/I4405259317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148784300","display_name":"Jheng-Jie Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Chen, Jheng-Jie","raw_affiliation_strings":["Faculty of Mathematics , Kyushu University , Fukuoka 819-0395 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics , Kyushu University , Fukuoka 819-0395 , Japan","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031087343","display_name":"Takuzo Okada","orcid":"https://orcid.org/0000-0002-7961-2258","observed_orcids":["https://orcid.org/0000-0002-7961-2258"]},"institutions":[{"id":"https://openalex.org/I22265921","display_name":"National Central University","ror":"https://ror.org/00944ve71","country_code":"TW","type":"education","lineage":["https://openalex.org/I22265921"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Okada, Takuzo","raw_affiliation_strings":["Department of Mathematics , National Central University , Taoyuan City , 320 , Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , National Central University , Taoyuan City , 320 , Taiwan","institution_ids":["https://openalex.org/I22265921"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9976000189781189,"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":0.9976000189781189,"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/T12351","display_name":"Geometry and complex manifolds","score":0.00139999995008111,"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":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/isolated-singularities","display_name":"isolated singularities","score":0.7329999804496765},{"id":"https://openalex.org/keywords/local-inequality","display_name":"local inequality","score":0.8460000157356262},{"id":"https://openalex.org/keywords/sharp-inequalities","display_name":"sharp inequalities","score":0.7670000195503235},{"id":"https://openalex.org/keywords/birational-rigidity","display_name":"birational rigidity","score":0.8379999995231628},{"id":"https://openalex.org/keywords/fano-threefolds","display_name":"Fano threefolds","score":0.9539999961853027},{"id":"https://openalex.org/keywords/weighted-hypersurfaces","display_name":"weighted hypersurfaces","score":0.9980000257492065}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.8456000089645386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7480000257492065},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7124999761581421},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6942999958992004},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5817000269889832},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5627999901771545},{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.5579000115394592},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5557000041007996},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C207769094","wikidata":"https://www.wikidata.org/wiki/Q4245771","display_name":"Singularity theory","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C143904861","wikidata":"https://www.wikidata.org/wiki/Q2297037","display_name":"Isolated singularity","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C71383303","wikidata":"https://www.wikidata.org/wiki/Q1876526","display_name":"Essential singularity","level":3,"score":0.26809999346733093},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.25780001282691956}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28372","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28372","pdf_url":"https://arxiv.org/pdf/2608.28372","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.28372","doi":"https://doi.org/10.48550/arxiv.2608.28372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28372","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28372","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28372","pdf_url":"https://arxiv.org/pdf/2608.28372","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","license_id":"https://openalex.org/licenses/cc-by","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/W7204790760.pdf","grobid_xml":"https://content.openalex.org/works/W7204790760.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4415993150"],"related_works":["https://openalex.org/W4415993150","https://openalex.org/W4399137969","https://openalex.org/W2908378045","https://openalex.org/W1966347971","https://openalex.org/W2276961612","https://openalex.org/W2120627704","https://openalex.org/W1580490410","https://openalex.org/W7117533742","https://openalex.org/W3102365430","https://openalex.org/W2952016175"],"abstract_inverted_index":{"We":[0],"obtain":[1],"inequalities":[2,22],"for":[3,15],"isolated":[4,16],"$cD_n,":[5],"cE_6,":[6],"cE_7$":[7],"and":[8,47],"$cE_8$":[9],"singularities,":[10],"analogues":[11],"of":[12,33,36],"the":[13,30],"$4\u03bc^2/(n+1)$-inequality":[14],"$cA_n$":[17],"singularity":[18],"in":[19],"\\cite{KOP}.":[20],"These":[21],"are":[23],"sharp.":[24],"This":[25],"enables":[26],"us":[27],"to":[28],"prove":[29],"birational":[31],"rigidity":[32],"certain":[34],"families":[35],"Fano":[37],"$3$-fold":[38],"weighted":[39],"hypersurfaces,":[40],"which":[41],"contain":[42],"only":[43],"terminal":[44],"quotient":[45],"singularities":[46],"one":[48],"$cD_n$":[49],"singularity.":[50]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}