{"id":"https://openalex.org/W4392600461","doi":"https://doi.org/10.1142/s0218196724500140","title":"Bounding embedded singularities of Hilbert schemes of points on affine three space","display_name":"Bounding embedded singularities of Hilbert schemes of points on affine three space","publication_year":2024,"publication_date":"2024-03-08","ids":{"openalex":"https://openalex.org/W4392600461","doi":"https://doi.org/10.1142/s0218196724500140"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196724500140","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218196724500140","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071680909","display_name":"Jen-Chieh Hsiao","orcid":"https://orcid.org/0000-0001-7244-8312"},"institutions":[{"id":"https://openalex.org/I91807558","display_name":"National Cheng Kung University","ror":"https://ror.org/01b8kcc49","country_code":"TW","type":"education","lineage":["https://openalex.org/I91807558"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Jen-Chieh Hsiao","raw_affiliation_strings":["Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan"],"raw_orcid":"https://orcid.org/0000-0001-7244-8312","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan","institution_ids":["https://openalex.org/I91807558"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071680909"],"corresponding_institution_ids":["https://openalex.org/I91807558"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05207317,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"03","first_page":"397","last_page":"405"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9247000217437744,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9247000217437744,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.931846022605896},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.666585385799408},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6504698395729065},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6482102274894714},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5428760647773743},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4533213973045349},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.45309334993362427},{"id":"https://openalex.org/keywords/affine-plane","display_name":"Affine plane (incidence geometry)","score":0.4307229816913605},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41969162225723267},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1877097487449646},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.054788291454315186},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04989403486251831}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.931846022605896},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.666585385799408},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6504698395729065},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6482102274894714},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5428760647773743},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4533213973045349},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.45309334993362427},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.4307229816913605},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41969162225723267},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1877097487449646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.054788291454315186},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04989403486251831},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196724500140","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218196724500140","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1495331326","https://openalex.org/W1638210929","https://openalex.org/W1988725437","https://openalex.org/W1994327923","https://openalex.org/W2057474290","https://openalex.org/W2118380482","https://openalex.org/W2951669235","https://openalex.org/W2992297556","https://openalex.org/W3101138499","https://openalex.org/W3103841012","https://openalex.org/W3174636784","https://openalex.org/W4245143666","https://openalex.org/W4249549360"],"related_works":["https://openalex.org/W1990737873","https://openalex.org/W4232695553","https://openalex.org/W3021421366","https://openalex.org/W2067039815","https://openalex.org/W2798263748","https://openalex.org/W3022853753","https://openalex.org/W2916011546","https://openalex.org/W2606958405","https://openalex.org/W2901311998","https://openalex.org/W1972070698"],"abstract_inverted_index":{"The":[0],"Hilbert":[1],"scheme":[2,63],"[Formula:":[3,10,28,44,58,64,70,81,92,96,102,112,120],"see":[4,11,29,45,59,65,71,82,88,93,97,103,113,121],"text]":[5,12,46,60,66,72,94,98,114],"of":[6,20,39,41,67,80,108],"n":[7],"points":[8,110],"on":[9,24,111],"can":[13],"be":[14],"expressed":[15],"as":[16],"the":[17,42,62,76,105],"critical":[18],"locus":[19],"a":[21,25,37,55,85],"regular":[22],"function":[23],"smooth":[26],"variety":[27],"text].":[30,83,122],"Recent":[31],"development":[32],"in":[33],"birational":[34],"geometry":[35],"suggests":[36],"study":[38],"singularities":[40],"pair":[43],"using":[47],"jet":[48],"schemes.":[49],"In":[50],"this":[51],"paper,":[52],"we":[53,87],"use":[54],"comparison":[56],"between":[57],"and":[61,95],"three":[68],"commuting":[69],"matrices":[73],"to":[74],"estimate":[75],"log":[77],"canonical":[78],"threshold":[79],"As":[84],"consequence,":[86],"that":[89],"although":[90],"both":[91],"have":[99],"asymptotic":[100],"growth":[101,119],"text],":[104],"largest":[106],"multiplicity":[107],"any":[109],"has":[115],"at":[116],"most":[117],"linear":[118]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}