{"id":"https://openalex.org/W1499496688","doi":"https://doi.org/10.37236/580","title":"Extensions of Toric Varieties","display_name":"Extensions of Toric Varieties","publication_year":2011,"publication_date":"2011-04-21","ids":{"openalex":"https://openalex.org/W1499496688","doi":"https://doi.org/10.37236/580","mag":"1499496688"},"language":"en","primary_location":{"id":"doi:10.37236/580","is_oa":true,"landing_page_url":"https://doi.org/10.37236/580","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p93/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p93/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025667894","display_name":"Mesut \u015eahi\u0307n","orcid":"https://orcid.org/0000-0002-0310-2542"},"institutions":[{"id":"https://openalex.org/I224962290","display_name":"\u00c7ank\u0131r\u0131 Karatekin University","ror":"https://ror.org/011y7xt38","country_code":"TR","type":"education","lineage":["https://openalex.org/I224962290"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Mesut \u015eahin","raw_affiliation_strings":["Cankiri Karatekin University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cankiri Karatekin University","institution_ids":["https://openalex.org/I224962290"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025667894"],"corresponding_institution_ids":["https://openalex.org/I224962290"],"apc_list":null,"apc_paid":null,"fwci":1.0536,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7023443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998000264167786,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9797999858856201,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9513999819755554,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9024122953414917},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.741585373878479},{"id":"https://openalex.org/keywords/complete-intersection","display_name":"Complete intersection","score":0.6644622683525085},{"id":"https://openalex.org/keywords/tangent-cone","display_name":"Tangent cone","score":0.6614476442337036},{"id":"https://openalex.org/keywords/toric-variety","display_name":"Toric variety","score":0.6563307046890259},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5966151356697083},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.595491886138916},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5564348697662354},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5436536073684692},{"id":"https://openalex.org/keywords/hilbert-series-and-hilbert-polynomial","display_name":"Hilbert series and Hilbert polynomial","score":0.509648323059082},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5082449316978455},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.49060454964637756},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40821224451065063},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.3745429217815399},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3309412896633148},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.13038411736488342},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08068972826004028},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06571465730667114},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0639050304889679}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9024122953414917},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.741585373878479},{"id":"https://openalex.org/C37253","wikidata":"https://www.wikidata.org/wiki/Q5156502","display_name":"Complete intersection","level":2,"score":0.6644622683525085},{"id":"https://openalex.org/C149944404","wikidata":"https://www.wikidata.org/wiki/Q2392464","display_name":"Tangent cone","level":3,"score":0.6614476442337036},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.6563307046890259},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5966151356697083},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.595491886138916},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5564348697662354},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5436536073684692},{"id":"https://openalex.org/C57033185","wikidata":"https://www.wikidata.org/wiki/Q5761236","display_name":"Hilbert series and Hilbert polynomial","level":3,"score":0.509648323059082},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5082449316978455},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.49060454964637756},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40821224451065063},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.3745429217815399},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3309412896633148},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.13038411736488342},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08068972826004028},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06571465730667114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0639050304889679},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/580","is_oa":true,"landing_page_url":"https://doi.org/10.37236/580","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p93/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/580","is_oa":true,"landing_page_url":"https://doi.org/10.37236/580","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p93/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1499496688.pdf","grobid_xml":"https://content.openalex.org/works/W1499496688.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1591331750","https://openalex.org/W1965161844","https://openalex.org/W1996311834","https://openalex.org/W2011284617","https://openalex.org/W2019312990","https://openalex.org/W2025225717","https://openalex.org/W2028512252","https://openalex.org/W2044872762","https://openalex.org/W2052636077","https://openalex.org/W2054381763","https://openalex.org/W2056827059","https://openalex.org/W2063168069","https://openalex.org/W2066181227","https://openalex.org/W2068011623","https://openalex.org/W2081445959","https://openalex.org/W2094169545","https://openalex.org/W2158314831","https://openalex.org/W2159354723","https://openalex.org/W2950996016","https://openalex.org/W4233144402","https://openalex.org/W4285719527","https://openalex.org/W4300166240"],"related_works":["https://openalex.org/W2610307711","https://openalex.org/W1754393280","https://openalex.org/W4254702043","https://openalex.org/W4239576438","https://openalex.org/W4250158467","https://openalex.org/W2765895272","https://openalex.org/W4297748950","https://openalex.org/W4299494264","https://openalex.org/W2950491727","https://openalex.org/W1499496688"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"the":[5,61],"notion":[6],"of":[7,9],"\"extension\"":[8],"a":[10,27,43,48],"toric":[11,24],"variety":[12],"and":[13,41,70],"study":[14],"its":[15],"fundamental":[16],"properties.":[17],"This":[18],"gives":[19],"rise":[20],"to":[21],"infinitely":[22],"many":[23],"varieties":[25],"with":[26,51,60],"special":[28],"property,":[29,63],"such":[30],"as":[31],"being":[32],"set":[33],"theoretic":[34],"complete":[35],"intersection":[36],"or":[37,47],"arithmetically":[38],"Cohen-Macaulay":[39,44],"(Gorenstein)":[40],"having":[42],"tangent":[45],"cone":[46],"local":[49],"ring":[50],"non-decreasing":[52],"Hilbert":[53],"function,":[54],"from":[55],"just":[56],"one":[57],"single":[58],"example":[59],"same":[62],"verifying":[64],"Rossi's":[65],"conjecture":[66],"for":[67],"larger":[68],"classes":[69],"extending":[71],"some":[72],"results":[73],"appeared":[74],"in":[75],"literature.":[76]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}