{"id":"https://openalex.org/W1797309881","doi":"https://doi.org/10.1090/mcom/2989","title":"Computing Cox rings","display_name":"Computing Cox rings","publication_year":2015,"publication_date":"2015-06-10","ids":{"openalex":"https://openalex.org/W1797309881","doi":"https://doi.org/10.1090/mcom/2989","mag":"1797309881"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/2989","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/2989","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10533/232464","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112763275","display_name":"J\u00fcrgen Hausen","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J\u00fcrgen Hausen","raw_affiliation_strings":["Mathematisches Institut, Universit\u00c3\u00a4t T\u00c3\u00bcbingen, Auf der Morgenstelle 10, 72076 T\u00c3\u00bcbingen, Germany","Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, 72076\u2009T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00c3\u00a4t T\u00c3\u00bcbingen, Auf der Morgenstelle 10, 72076 T\u00c3\u00bcbingen, Germany","institution_ids":[]},{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, 72076\u2009T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020447529","display_name":"Simon Keicher","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Simon Keicher","raw_affiliation_strings":["Mathematisches Institut, Universit\u00c3\u00a4t T\u00c3\u00bcbingen, Auf der Morgenstelle 10, 72076 T\u00c3\u00bcbingen, Germany","Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, 72076\u2009T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00c3\u00a4t T\u00c3\u00bcbingen, Auf der Morgenstelle 10, 72076 T\u00c3\u00bcbingen, Germany","institution_ids":[]},{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, 72076\u2009T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055936436","display_name":"Antonio Laface","orcid":"https://orcid.org/0000-0001-6926-8249"},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Antonio Laface","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1tica, Universidad de Concepci\u00c3\u00b3n, Casilla 160-C, Concepci\u00c3\u00b3n, Chile","Departamento de Matem\u00e1tica; Universidad de Concepci\u00f3n; Casilla 160-C Concepci\u00f3n Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1tica, Universidad de Concepci\u00c3\u00b3n, Casilla 160-C, Concepci\u00c3\u00b3n, Chile","institution_ids":[]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica; Universidad de Concepci\u00f3n; Casilla 160-C Concepci\u00f3n Chile","institution_ids":["https://openalex.org/I172787465"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.4835,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.95881832,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"85","issue":"297","first_page":"467","last_page":"502"},"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":0.9991999864578247,"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":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7105539441108704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6925792098045349},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.556244432926178},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5559741854667664},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45032113790512085},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.42857807874679565},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3660132884979248},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.342120885848999},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09608018398284912},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05755627155303955}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7105539441108704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6925792098045349},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.556244432926178},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5559741854667664},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45032113790512085},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.42857807874679565},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3660132884979248},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.342120885848999},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09608018398284912},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05755627155303955},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/2989","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/2989","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:localhost:10533/232464","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/232464","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics Of Computation","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1305.4343","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1305.4343","pdf_url":"https://arxiv.org/pdf/1305.4343","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:americanae.aecid.es:3237661","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3237661","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Of Computation","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:localhost:10533/232464","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/232464","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics Of Computation","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W26737174","https://openalex.org/W1031017996","https://openalex.org/W1483731757","https://openalex.org/W1528422837","https://openalex.org/W1537258143","https://openalex.org/W1565608467","https://openalex.org/W1568502052","https://openalex.org/W1573089828","https://openalex.org/W1580842374","https://openalex.org/W1585144295","https://openalex.org/W1607468127","https://openalex.org/W1615336570","https://openalex.org/W1653585802","https://openalex.org/W1683805643","https://openalex.org/W1863750938","https://openalex.org/W1963563958","https://openalex.org/W1976677460","https://openalex.org/W1986845759","https://openalex.org/W2012922149","https://openalex.org/W2028323364","https://openalex.org/W2035352599","https://openalex.org/W2043888222","https://openalex.org/W2049388254","https://openalex.org/W2049397242","https://openalex.org/W2049841614","https://openalex.org/W2052532747","https://openalex.org/W2057245894","https://openalex.org/W2066181227","https://openalex.org/W2081659888","https://openalex.org/W2085918896","https://openalex.org/W2086090046","https://openalex.org/W2096571745","https://openalex.org/W2120360705","https://openalex.org/W2131073910","https://openalex.org/W2162349846","https://openalex.org/W2175098281","https://openalex.org/W2223977722","https://openalex.org/W2258062532","https://openalex.org/W2339507371","https://openalex.org/W2498144018","https://openalex.org/W2909039029","https://openalex.org/W2950391053","https://openalex.org/W2952350510","https://openalex.org/W2963115589","https://openalex.org/W2964016655","https://openalex.org/W2964220995","https://openalex.org/W3037024206","https://openalex.org/W3102403861","https://openalex.org/W3155258486","https://openalex.org/W4212938781","https://openalex.org/W4244479785","https://openalex.org/W4253316146","https://openalex.org/W4300166240"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3124916295","https://openalex.org/W2022411416","https://openalex.org/W2167530280","https://openalex.org/W2146447767","https://openalex.org/W1487790116","https://openalex.org/W3197597876","https://openalex.org/W4248544590","https://openalex.org/W1529020016","https://openalex.org/W4381247976"],"abstract_inverted_index":{"We":[0],"consider":[1],"modifications,":[2],"for":[3,14,22,86],"example":[4,23],"blow":[5],"ups,":[6],"of":[7,34,47,54,67,82,99],"Mori":[8,74],"dream":[9,75],"spaces":[10,101],"and":[11,36,77],"provide":[12,79,95],"algorithms":[13],"investigating":[15],"the":[16,19,44,83,96],"effect":[17],"on":[18],"Cox":[20,45,84,97],"ring,":[21],"verifying":[24],"finite":[25],"generation":[26],"or":[27],"computing":[28],"an":[29],"explicit":[30,80],"presentation":[31],"in":[32],"terms":[33],"generators":[35],"relations.":[37],"As":[38],"a":[39,90],"first":[40],"application,":[41],"we":[42,59,78,94],"compute":[43],"rings":[46,98],"all":[48,63],"Gorenstein":[49],"log":[50],"del":[51],"Pezzo":[52],"surfaces":[53,66,76],"Picard":[55,68],"number":[56],"one.":[57],"Moreover,":[58],"show":[60],"computationally":[61],"that":[62],"smooth":[64],"rational":[65],"numbers":[69],"at":[70,104],"most":[71],"six":[72],"are":[73],"presentations":[81],"ring":[85],"those":[87],"not":[88],"admitting":[89],"torus":[91],"action.":[92],"Finally,":[93],"projective":[100],"blown":[102],"up":[103],"certain":[105],"special":[106],"point":[107],"configurations.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}