{"id":"https://openalex.org/W1987664981","doi":"https://doi.org/10.1142/s021819671250049x","title":"COMPLETE INTERSECTIONS AND MOVABLE CURVES ON THE MODULI SPACE OF SIX-POINTED RATIONAL CURVES","display_name":"COMPLETE INTERSECTIONS AND MOVABLE CURVES ON THE MODULI SPACE OF SIX-POINTED RATIONAL CURVES","publication_year":2012,"publication_date":"2012-05-17","ids":{"openalex":"https://openalex.org/W1987664981","doi":"https://doi.org/10.1142/s021819671250049x","mag":"1987664981"},"language":"en","primary_location":{"id":"doi:10.1142/s021819671250049x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671250049x","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/A5077692169","display_name":"Paul L. Larsen","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"PAUL L. LARSEN","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, 10099 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, 10099 Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5077692169"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06279468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"06","first_page":"1250049","last_page":"1250049"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9980000257492065,"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":0.9962999820709229,"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/mathematics","display_name":"Mathematics","score":0.8456858396530151},{"id":"https://openalex.org/keywords/moduli-space","display_name":"Moduli space","score":0.8414335250854492},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6879656314849854},{"id":"https://openalex.org/keywords/family-of-curves","display_name":"Family of curves","score":0.6662979125976562},{"id":"https://openalex.org/keywords/toric-variety","display_name":"Toric variety","score":0.6186670064926147},{"id":"https://openalex.org/keywords/intersection-theory","display_name":"Intersection theory","score":0.6162078380584717},{"id":"https://openalex.org/keywords/twisted-cubic","display_name":"Twisted cubic","score":0.5653347969055176},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5471417903900146},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.5443333387374878},{"id":"https://openalex.org/keywords/moduli-of-algebraic-curves","display_name":"Moduli of algebraic curves","score":0.5267124772071838},{"id":"https://openalex.org/keywords/complete-intersection","display_name":"Complete intersection","score":0.5243756771087646},{"id":"https://openalex.org/keywords/projective-space","display_name":"Projective space","score":0.5207191109657288},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5013127326965332},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49703148007392883},{"id":"https://openalex.org/keywords/projective-variety","display_name":"Projective variety","score":0.48889580368995667},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.48880884051322937},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.4265179932117462},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3309890031814575},{"id":"https://openalex.org/keywords/complex-projective-space","display_name":"Complex projective space","score":0.24746796488761902},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.2348865568637848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.060488373041152954},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.05699962377548218}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8456858396530151},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.8414335250854492},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6879656314849854},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.6662979125976562},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.6186670064926147},{"id":"https://openalex.org/C77462122","wikidata":"https://www.wikidata.org/wiki/Q15176852","display_name":"Intersection theory","level":5,"score":0.6162078380584717},{"id":"https://openalex.org/C37500760","wikidata":"https://www.wikidata.org/wiki/Q7858555","display_name":"Twisted cubic","level":5,"score":0.5653347969055176},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5471417903900146},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.5443333387374878},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.5267124772071838},{"id":"https://openalex.org/C37253","wikidata":"https://www.wikidata.org/wiki/Q5156502","display_name":"Complete intersection","level":2,"score":0.5243756771087646},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.5207191109657288},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5013127326965332},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49703148007392883},{"id":"https://openalex.org/C62139920","wikidata":"https://www.wikidata.org/wiki/Q3554818","display_name":"Projective variety","level":2,"score":0.48889580368995667},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.48880884051322937},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.4265179932117462},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3309890031814575},{"id":"https://openalex.org/C132702353","wikidata":"https://www.wikidata.org/wiki/Q2538404","display_name":"Complex projective space","level":4,"score":0.24746796488761902},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.2348865568637848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.060488373041152954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.05699962377548218},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"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/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819671250049x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671250049x","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":[{"id":"https://metadata.un.org/sdg/11","score":0.7300000190734863,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W954650338","https://openalex.org/W1965797498","https://openalex.org/W1983953462","https://openalex.org/W2000098711","https://openalex.org/W2025499050","https://openalex.org/W2053346979","https://openalex.org/W2066504038","https://openalex.org/W2962988534","https://openalex.org/W4205502224","https://openalex.org/W4248269519"],"related_works":["https://openalex.org/W1997490652","https://openalex.org/W3098925533","https://openalex.org/W2949580718","https://openalex.org/W4390512259","https://openalex.org/W2017700406","https://openalex.org/W3122238028","https://openalex.org/W4381827779","https://openalex.org/W1987664981","https://openalex.org/W2950272672","https://openalex.org/W4297908324"],"abstract_inverted_index":{"A":[0],"curve":[1],"on":[2,44],"a":[3,45,122],"projective":[4,51,123],"variety":[5],"is":[6,76,107],"called":[7],"movable":[8,27,79],"if":[9],"it":[10],"belongs":[11],"to":[12],"an":[13,109,119],"algebraic":[14],"family":[15,46],"of":[16,26,35,47,49,57,69,89,101,121],"curves":[17,28,61],"covering":[18,36],"the":[19,24,40,54,63,78,86,95,98],"variety.":[20],"We":[21,116],"consider":[22],"when":[23],"cone":[25,43],"can":[29],"be":[30],"characterized":[31],"without":[32],"existence":[33],"statements":[34],"families":[37],"by":[38],"studying":[39],"complete":[41,81],"intersection":[42,82],"blow-ups":[48],"complex":[50],"space,":[52],"including":[53],"moduli":[55,67,99],"space":[56,68,100],"stable":[58],"six-pointed":[59,102],"rational":[60,71,103],"and":[62,80],"permutohedral":[64],"or":[65],"Losev\u2013Manin":[66],"four-pointed":[70],"curves.":[72,104],"Our":[73],"main":[74],"result":[75],"that":[77,111],"cones":[83,130],"coincide":[84],"for":[85,94,126],"toric":[87,124],"members":[88],"this":[90],"family,":[91],"but":[92],"differ":[93],"non-toric":[96],"member,":[97],"The":[105],"proof":[106],"via":[108],"algorithm":[110],"applies":[112],"in":[113],"greater":[114],"generality.":[115],"also":[117],"give":[118],"example":[120],"threefold":[125],"which":[127],"these":[128],"two":[129],"differ.":[131]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
