{"id":"https://openalex.org/W2905051142","doi":"https://doi.org/10.1080/10586458.2021.1978117","title":"A Construction of Multiplicity Class of Hypersurfaces From Hesselink Stratification of a Hilbert Scheme","display_name":"A Construction of Multiplicity Class of Hypersurfaces From Hesselink Stratification of a Hilbert Scheme","publication_year":2021,"publication_date":"2021-10-07","ids":{"openalex":"https://openalex.org/W2905051142","doi":"https://doi.org/10.1080/10586458.2021.1978117","mag":"2905051142"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2021.1978117","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1978117","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.06730","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066035433","display_name":"Lee Cheol-Gyu","orcid":null},"institutions":[{"id":"https://openalex.org/I125608817","display_name":"Korea Institute for Advanced Study","ror":"https://ror.org/041hz9568","country_code":"KR","type":"facility","lineage":["https://openalex.org/I125608817"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Cheolgyu Lee","raw_affiliation_strings":["School of Mathematics, Korea Institute for Advanced Study(KIAS), Seoul, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Korea Institute for Advanced Study(KIAS), Seoul, Republic of Korea","institution_ids":["https://openalex.org/I125608817"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066035433"],"corresponding_institution_ids":["https://openalex.org/I125608817"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01528853,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"2","first_page":"423","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9951000213623047,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9901999831199646,"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/hypersurface","display_name":"Hypersurface","score":0.9139912128448486},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.9059070944786072},{"id":"https://openalex.org/keywords/stratification","display_name":"Stratification (seeds)","score":0.7689130306243896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7137763500213623},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.5643341541290283},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5606029629707336},{"id":"https://openalex.org/keywords/hilbert-scheme","display_name":"Hilbert scheme","score":0.522102952003479},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.383650541305542}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.9139912128448486},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.9059070944786072},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.7689130306243896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7137763500213623},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.5643341541290283},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5606029629707336},{"id":"https://openalex.org/C150279058","wikidata":"https://www.wikidata.org/wiki/Q5761225","display_name":"Hilbert scheme","level":2,"score":0.522102952003479},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.383650541305542},{"id":"https://openalex.org/C88548481","wikidata":"https://www.wikidata.org/wiki/Q2397491","display_name":"Seed dormancy","level":4,"score":0.0},{"id":"https://openalex.org/C3527866","wikidata":"https://www.wikidata.org/wiki/Q162267","display_name":"Dormancy","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C100701293","wikidata":"https://www.wikidata.org/wiki/Q193838","display_name":"Germination","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2021.1978117","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1978117","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1811.06730","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.06730","pdf_url":"https://arxiv.org/pdf/1811.06730","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"mag:2905051142","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1811.06730.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1811.06730","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.06730","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.06730","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.06730","pdf_url":"https://arxiv.org/pdf/1811.06730","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[{"id":"https://openalex.org/F5450473328","display_name":"Korea Institute for Advanced Study","ror":"https://ror.org/041hz9568"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1551578848","https://openalex.org/W1620508573","https://openalex.org/W2017573057","https://openalex.org/W2026853928","https://openalex.org/W2239958466","https://openalex.org/W2606736397"],"related_works":["https://openalex.org/W2951412103","https://openalex.org/W1567149624","https://openalex.org/W1545771371","https://openalex.org/W1596154176","https://openalex.org/W2564159249","https://openalex.org/W3086453692","https://openalex.org/W2963242901","https://openalex.org/W2964318141","https://openalex.org/W1999759055","https://openalex.org/W2145173584","https://openalex.org/W3093155958","https://openalex.org/W2949334918","https://openalex.org/W2061915121","https://openalex.org/W1636981115","https://openalex.org/W2018263856","https://openalex.org/W2787156918","https://openalex.org/W2962707209","https://openalex.org/W2052841982","https://openalex.org/W3028915518","https://openalex.org/W1604078192"],"abstract_inverted_index":{"It":[0],"is":[1,6],"well":[2],"known":[3],"that":[4],"there":[5],"a":[7,23,45],"positive":[8],"relationship":[9],"between":[10],"the":[11,15,32,41],"maximal":[12],"multiplicity":[13,33],"and":[14,37],"length":[16],"of":[17,22,35,44],"associated":[18],"virtual":[19],"1-parameter":[20],"subgroup":[21],"projective":[24],"hypersurface.":[25],"In":[26],"this":[27],"article,":[28],"we":[29],"will":[30],"define":[31],"classes":[34],"hypersurfaces":[36],"construct":[38],"them":[39],"from":[40],"Hesselink":[42],"stratification":[43],"Hilbert":[46],"scheme.":[47]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2018-12-22T00:00:00"}
