{"id":"https://openalex.org/W7125782996","doi":"https://doi.org/10.1090/mcom/4143","title":"Discrete geometry of Cox rings of blow-ups of \u2119\u00b3","display_name":"Discrete geometry of Cox rings of blow-ups of \u2119\u00b3","publication_year":2026,"publication_date":"2026-01-27","ids":{"openalex":"https://openalex.org/W7125782996","doi":"https://doi.org/10.1090/mcom/4143"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4143","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4143","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":["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/A5123931042","display_name":"Mara Belotti","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mara Belotti","raw_affiliation_strings":["Discrete Mathematics/Geometry, Technische Universit\u00e4t, Institut f\u00fcr Mathematik der Technischen Universit\u00e4t Berlin, Sekretariat MA 6-2, Stra\u00dfe des 17. Juni 136, 10623 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Discrete Mathematics/Geometry, Technische Universit\u00e4t, Institut f\u00fcr Mathematik der Technischen Universit\u00e4t Berlin, Sekretariat MA 6-2, Stra\u00dfe des 17. Juni 136, 10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018660404","display_name":"Marta Panizzut","orcid":"https://orcid.org/0000-0001-8631-6329"},"institutions":[{"id":"https://openalex.org/I4210091523","display_name":"Forskning.no (Norway)","ror":"https://ror.org/00c9dk124","country_code":"NO","type":"company","lineage":["https://openalex.org/I4210091523"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Marta Panizzut","raw_affiliation_strings":["UiT - The Artic University of Norway, Forskningsparken 1, 9037 Troms\u00f8, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UiT - The Artic University of Norway, Forskningsparken 1, 9037 Troms\u00f8, Norway","institution_ids":["https://openalex.org/I4210091523"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18801734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"362","first_page":"3081","last_page":"3100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.7328000068664551,"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":0.7328000068664551,"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":0.11060000211000443,"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":0.07970000058412552,"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/polytope","display_name":"Polytope","score":0.9003999829292297},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6703000068664551},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6486999988555908},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5329999923706055},{"id":"https://openalex.org/keywords/toric-variety","display_name":"Toric variety","score":0.4562000036239624},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.45559999346733093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9041000008583069},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9003999829292297},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6703000068664551},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6486999988555908},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5329999923706055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5074999928474426},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.4562000036239624},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.45559999346733093},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4542999863624573},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3528999984264374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3303000032901764},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.31700000166893005},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.2800000011920929},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4143","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4143","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W2034410660","https://openalex.org/W2038338285","https://openalex.org/W2045009680","https://openalex.org/W2052532747","https://openalex.org/W2057245894","https://openalex.org/W2120360705","https://openalex.org/W2197803292","https://openalex.org/W2962882481","https://openalex.org/W2962901410","https://openalex.org/W2963221791","https://openalex.org/W2963955378","https://openalex.org/W2964220995","https://openalex.org/W2964233928","https://openalex.org/W3164217733","https://openalex.org/W4206077821","https://openalex.org/W4234523432","https://openalex.org/W4249549360","https://openalex.org/W4293097209"],"related_works":[],"abstract_inverted_index":{"We":[0,69],"prove":[1],"quadratic":[2],"generation":[3],"for":[4],"the":[5,8,12,43,71,79],"ideal":[6],"of":[7,11,14,26,45,73],"Cox":[9],"ring":[10],"blow-up":[13],"P":[15],"3":[16],"\\mathbb":[17],"{P}^3":[18],"at":[19],"7":[20,21],"points,":[22],"solving":[23],"a":[24],"conjecture":[25],"Lesieutre":[27],"and":[28,76],"Park.":[29],"To":[30],"do":[31],"this":[32],"we":[33,77],"compute":[34],"Khovanskii":[35],"bases,":[36],"implementing":[37],"techniques":[38],"which":[39],"proved":[40],"successful":[41],"in":[42],"case":[44],"del":[46],"Pezzo":[47],"surfaces.":[48],"Such":[49],"bases":[50],"give":[51],"us":[52],"degenerations":[53,62],"to":[54,65],"toric":[55,61],"varieties":[56],"whose":[57],"associated":[58],"polytopes":[59,75],"encode":[60],"with":[63],"respect":[64],"all":[66],"projective":[67],"embeddings.":[68],"study":[70],"edge-graphs":[72],"these":[74],"introduce":[78],"Mukai":[80],"edge":[81],"graph":[82],".":[83]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-01-28T00:00:00"}
