{"id":"https://openalex.org/W3200679341","doi":"https://doi.org/10.1137/22m1475533","title":"Complex Links and Hilbert\u2013Samuel Multiplicities","display_name":"Complex Links and Hilbert\u2013Samuel Multiplicities","publication_year":2023,"publication_date":"2023-03-08","ids":{"openalex":"https://openalex.org/W3200679341","doi":"https://doi.org/10.1137/22m1475533","mag":"3200679341"},"language":"en","primary_location":{"id":"doi:10.1137/22m1475533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1475533","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","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/A5018927033","display_name":"Martin Helmer","orcid":"https://orcid.org/0000-0002-9170-8295"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin Helmer","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069873248","display_name":"Vidit Nanda","orcid":"https://orcid.org/0000-0001-9243-6749"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Vidit Nanda","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, UK, OX2 6GG"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, UK, OX2 6GG","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3454,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58397524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"7","issue":"1","first_page":"29","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9951000213623047,"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":0.9681000113487244,"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/hyperplane","display_name":"Hyperplane","score":0.8221983313560486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7321267127990723},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6816336512565613},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6727872490882874},{"id":"https://openalex.org/keywords/euler-characteristic","display_name":"Euler characteristic","score":0.5994833111763},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5482129454612732},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5239008665084839},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4935067892074585},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45356106758117676},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.419597327709198},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3224799633026123},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2778564989566803},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2541393041610718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12520593404769897},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12293094396591187}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8221983313560486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7321267127990723},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6816336512565613},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6727872490882874},{"id":"https://openalex.org/C196433757","wikidata":"https://www.wikidata.org/wiki/Q852973","display_name":"Euler characteristic","level":2,"score":0.5994833111763},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5482129454612732},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5239008665084839},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4935067892074585},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45356106758117676},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.419597327709198},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3224799633026123},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2778564989566803},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2541393041610718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12520593404769897},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12293094396591187},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1475533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1475533","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:6f82b7f4-29d5-4fe6-b924-ee88c96755b9","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:6f82b7f4-29d5-4fe6-b924-ee88c96755b9","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1132496359","display_name":"Application driven Topological Data Analysis","funder_award_id":"EP/R018472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6066696820","display_name":null,"funder_award_id":"EP/R018472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W152813414","https://openalex.org/W204424931","https://openalex.org/W1498067247","https://openalex.org/W1512458023","https://openalex.org/W1536451965","https://openalex.org/W1570420806","https://openalex.org/W1968812687","https://openalex.org/W1982227707","https://openalex.org/W2011693299","https://openalex.org/W2054863674","https://openalex.org/W2075915700","https://openalex.org/W2155791330","https://openalex.org/W2157878484","https://openalex.org/W2500739438","https://openalex.org/W2606650290","https://openalex.org/W2912253187","https://openalex.org/W2952111492","https://openalex.org/W2964130118","https://openalex.org/W2997383166","https://openalex.org/W3047315483","https://openalex.org/W3094481448","https://openalex.org/W3103907078","https://openalex.org/W3175319937","https://openalex.org/W4213171111","https://openalex.org/W4231216667","https://openalex.org/W4234362625","https://openalex.org/W4241140300","https://openalex.org/W4300076833","https://openalex.org/W4300596011"],"related_works":["https://openalex.org/W2900918889","https://openalex.org/W2088544526","https://openalex.org/W3101175790","https://openalex.org/W2090054623","https://openalex.org/W3105528072","https://openalex.org/W2012868913","https://openalex.org/W2949062814","https://openalex.org/W3200679341","https://openalex.org/W4323657624","https://openalex.org/W2738729766"],"abstract_inverted_index":{"We":[0],"describe":[1],"a":[2,41,47],"framework":[3],"for":[4,9],"estimating":[5],"Hilbert\u2013Samuel":[6],"multiplicities":[7],"eXY":[8],"pairs":[10],"of":[11,63,67,79,88],"projective":[12],"varieties":[13],"X\u2282Y":[14],"from":[15],"finite":[16],"point":[17,42,81],"samples":[18,82],"rather":[19],"than":[20],"defining":[21],"equations.":[22],"The":[23],"first":[24],"step":[25],"involves":[26],"proving":[27],"that":[28,53],"this":[29,94],"multiplicity":[30],"remains":[31],"invariant":[32],"under":[33],"certain":[34],"hyperplane":[35],"sections":[36],"which":[37],"reduce":[38],"X":[39],"to":[40,46,92],"p":[43,68,89],"and":[44],"Y":[45],"curve":[48],"C.":[49,70],"Next,":[50],"we":[51,72],"establish":[52],"epC":[54],"equals":[55],"the":[56,61,64,77],"Euler":[57,95],"characteristic":[58,96],"(and":[59],"hence":[60],"cardinality)":[62],"complex":[65],"link":[66],"in":[69,90],"Finally,":[71],"provide":[73],"explicit":[74],"bounds":[75],"on":[76],"number":[78],"uniform":[80],"needed":[83],"(in":[84],"an":[85],"annular":[86],"neighborhood":[87],"C)":[91],"determine":[93],"with":[97],"high":[98],"confidence.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}