{"id":"https://openalex.org/W7208743455","doi":"https://doi.org/10.48550/arxiv.2609.04054","title":"An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds","display_name":"An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7208743455","doi":"https://doi.org/10.48550/arxiv.2609.04054"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04054","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04054","pdf_url":"https://arxiv.org/pdf/2609.04054","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/2609.04054","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075189669","display_name":"Fatemeh Rezaee","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rezaee, Fatemeh","raw_affiliation_strings":["CENTRE FOR MATHEMATICAL SCIENCES , UNIVERSITY OF CAMBRIDGE , WILBERFORCE ROAD , CB3 0WA , CAMBRIDGE , UNITED KINGDOM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CENTRE FOR MATHEMATICAL SCIENCES , UNIVERSITY OF CAMBRIDGE , WILBERFORCE ROAD , CB3 0WA , CAMBRIDGE , UNITED KINGDOM","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5150000015","display_name":"Parsa Saberi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Saberi, Parsa","raw_affiliation_strings":["CENTRE FOR MATHEMATICAL SCIENCES , UNIVERSITY OF CAMBRIDGE , WILBERFORCE ROAD , CB3 0WA , CAMBRIDGE , UNITED KINGDOM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CENTRE FOR MATHEMATICAL SCIENCES , UNIVERSITY OF CAMBRIDGE , WILBERFORCE ROAD , CB3 0WA , CAMBRIDGE , UNITED KINGDOM","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I241749"],"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":0.9932000041007996,"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":0.9932000041007996,"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":0.006000000052154064,"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/T12351","display_name":"Geometry and complex manifolds","score":0.00019999999494757503,"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/hilbert-scheme-of-points","display_name":"Hilbert schemes of points","score":0.9369999766349792},{"id":"https://openalex.org/keywords/threefolds","display_name":"threefolds","score":0.878000020980835},{"id":"https://openalex.org/keywords/tangent-space","display_name":"tangent space","score":0.7409999966621399},{"id":"https://openalex.org/keywords/gorenstein-ideals","display_name":"Gorenstein ideals","score":0.49300000071525574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8712999820709229},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.8259000182151794},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7476000189781189},{"id":"https://openalex.org/C71383303","wikidata":"https://www.wikidata.org/wiki/Q1876526","display_name":"Essential singularity","level":3,"score":0.572700023651123},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.572700023651123},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5656999945640564},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.4961000084877014},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4778999984264374},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C207769094","wikidata":"https://www.wikidata.org/wiki/Q4245771","display_name":"Singularity theory","level":3,"score":0.4325000047683716},{"id":"https://openalex.org/C143904861","wikidata":"https://www.wikidata.org/wiki/Q2297037","display_name":"Isolated singularity","level":3,"score":0.42800000309944153},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4043999910354614},{"id":"https://openalex.org/C150279058","wikidata":"https://www.wikidata.org/wiki/Q5761225","display_name":"Hilbert scheme","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3327000141143799},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2793999910354614},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.27570000290870667}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04054","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04054","pdf_url":"https://arxiv.org/pdf/2609.04054","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.2609.04054","doi":"https://doi.org/10.48550/arxiv.2609.04054","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04054","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:2609.04054","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04054","pdf_url":"https://arxiv.org/pdf/2609.04054","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/W7208743455.pdf","grobid_xml":"https://content.openalex.org/works/W7208743455.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W4403046938","https://openalex.org/W4403570974","https://openalex.org/W4403784770","https://openalex.org/W4406452646","https://openalex.org/W4415097637","https://openalex.org/W4415993186","https://openalex.org/W6948035254","https://openalex.org/W7203640627"],"related_works":["https://openalex.org/W4415993186","https://openalex.org/W4389500179","https://openalex.org/W6948035254","https://openalex.org/W2980320166","https://openalex.org/W4210885064","https://openalex.org/W2599320418","https://openalex.org/W4392600461","https://openalex.org/W2914059617","https://openalex.org/W4232169967","https://openalex.org/W2073857139"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,22,36,51,79],"necessary":[3],"condition":[4],"conjecture":[5],"([27,":[6],"Conjecture":[7,34],"B])":[8],"for":[9,21,35],"the":[10,14,31,42,56,59,63,73,83,92],"maximal":[11,75],"singularity":[12,76],"of":[13,17,25,58,62,85],"Hilbert":[15],"scheme":[16],"points":[18],"in":[19,28,44,49],"3D":[20],"large":[23],"class":[24],"degrees,":[26],"which":[27],"particular":[29],"implies":[30],"1978":[32],"Brian\u00e7on-Iarrobino":[33],"tetrahedral":[37],"degree,":[38],"and":[39,89],"vastly":[40],"generalises":[41],"result":[43],"[19].":[45],"The":[46],"novelty":[47],"lies":[48],"introducing":[50],"new":[52],"upper":[53],"bound":[54,81],"on":[55,82],"dimensions":[57],"tangent":[60,87],"spaces":[61],"claimed":[64,74],"non-maximally":[65],"singular":[66],"ideals,":[67],"constructing":[68],"canonical":[69],"ideals":[70],"that":[71],"satisfy":[72],"condition,":[77],"providing":[78],"lower":[80],"dimension":[84],"their":[86],"spaces,":[88],"finally":[90],"comparing":[91],"two":[93],"cases.":[94]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-05T00:00:00"}
