{"id":"https://openalex.org/W7214924244","doi":"https://doi.org/10.48550/arxiv.2609.36034","title":"Global Sections and Birational Geometry of Calabi-Yau Type Varieties","display_name":"Global Sections and Birational Geometry of Calabi-Yau Type Varieties","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214924244","doi":"https://doi.org/10.48550/arxiv.2609.36034"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36034","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36034","pdf_url":"https://arxiv.org/pdf/2609.36034","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.36034","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029287973","display_name":"Andrei Constantin","orcid":"https://orcid.org/0000-0002-0861-5363","observed_orcids":["https://orcid.org/0000-0002-0861-5363"]},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Constantin, Andrei","raw_affiliation_strings":["School of Mathematics , University of Birmingham , Watson Building , Edgbaston , Birmingham B15 2TT , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , University of Birmingham , Watson Building , Edgbaston , Birmingham B15 2TT , UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001303489","display_name":"Andr\u00e9 Lukas A","orcid":"https://orcid.org/0000-0003-4969-0447","observed_orcids":["https://orcid.org/0000-0003-4969-0447"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lukas, Andre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153582518","display_name":"Elijah Sheridan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sheridan, Elijah","raw_affiliation_strings":["School of Mathematics , University of Birmingham , Watson Building , Edgbaston , Birmingham B15 2TT , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , University of Birmingham , Watson Building , Edgbaston , Birmingham B15 2TT , UK","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9901999831199646,"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":0.9901999831199646,"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/T12351","display_name":"Geometry and complex manifolds","score":0.008299999870359898,"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":9.999999747378752e-05,"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/klt-singularities","display_name":"klt singularities","score":0.8700000047683716},{"id":"https://openalex.org/keywords/euler-characteristic","display_name":"Euler characteristic","score":0.621999979019165},{"id":"https://openalex.org/keywords/vanishing-theorems","display_name":"vanishing theorems","score":0.925000011920929},{"id":"https://openalex.org/keywords/big-divisors","display_name":"big divisors","score":0.6949999928474426},{"id":"https://openalex.org/keywords/movable-cone","display_name":"movable cone","score":0.8059999942779541},{"id":"https://openalex.org/keywords/effective-cone","display_name":"effective cone","score":0.8080000281333923},{"id":"https://openalex.org/keywords/birational-geometry","display_name":"birational geometry","score":0.7360000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8652999997138977},{"id":"https://openalex.org/C96881808","wikidata":"https://www.wikidata.org/wiki/Q1879333","display_name":"Birational geometry","level":2,"score":0.6721000075340271},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5389999747276306},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5333999991416931},{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.5285000205039978},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5127000212669373},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4699000120162964},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.43050000071525574},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C2777831296","wikidata":"https://www.wikidata.org/wiki/Q12518","display_name":"Tower","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C68060419","wikidata":"https://www.wikidata.org/wiki/Q40754","display_name":"Subtraction","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26080000400543213},{"id":"https://openalex.org/C2777767291","wikidata":"https://www.wikidata.org/wiki/Q1080291","display_name":"Sizing","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36034","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36034","pdf_url":"https://arxiv.org/pdf/2609.36034","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,"listed_in":[],"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":"doi:10.48550/arxiv.2609.36034","doi":"https://doi.org/10.48550/arxiv.2609.36034","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36034","pdf_url":null,"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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36034","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36034","pdf_url":"https://arxiv.org/pdf/2609.36034","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214924244.pdf","grobid_xml":"https://content.openalex.org/works/W7214924244.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1677296536","https://openalex.org/W1796115931","https://openalex.org/W2032485802","https://openalex.org/W2099716392","https://openalex.org/W2160385356","https://openalex.org/W2889066904","https://openalex.org/W2891834385","https://openalex.org/W2947577888","https://openalex.org/W2949671925","https://openalex.org/W2963800692","https://openalex.org/W3092970397","https://openalex.org/W3184757787","https://openalex.org/W3195181263","https://openalex.org/W4225626752","https://openalex.org/W4294200684","https://openalex.org/W4308668666","https://openalex.org/W4310224712","https://openalex.org/W4390268997","https://openalex.org/W4391334962","https://openalex.org/W4391347650","https://openalex.org/W4391718345","https://openalex.org/W4399597959","https://openalex.org/W4399783645","https://openalex.org/W4404988648","https://openalex.org/W7116048737","https://openalex.org/W7135200192","https://openalex.org/W7148657523","https://openalex.org/W7165690459","https://openalex.org/W7166506121"],"related_works":["https://openalex.org/W2973714960","https://openalex.org/W7100573248","https://openalex.org/W7064891678","https://openalex.org/W2079929412","https://openalex.org/W2032485802","https://openalex.org/W2760649476","https://openalex.org/W7143788080","https://openalex.org/W7098891118","https://openalex.org/W7166888060","https://openalex.org/W7096696290"],"abstract_inverted_index":{"We":[0,14,105],"investigate":[1],"aspects":[2,185],"of":[3,9,20,45,89,123,130,153,158,162,167,181,186],"the":[4,29,35,71,87,114,120,124,128,138,149,165,175,187,191],"relationship":[5],"between":[6],"global":[7,24,43,90,111,168],"sections":[8,25,44,112,169],"divisors":[10,48],"and":[11,190],"birational":[12,31,60,151,160,171,193],"geometry.":[13],"show":[15],"that":[16,33],"for":[17,110],"varieties":[18,133],"$X$":[19],"klt":[21],"Calabi-Yau":[22],"type,":[23],"are":[26,119],"governed":[27],"by":[28,77,94,98],"same":[30],"data":[32],"control":[34],"$D$-minimal":[36,103],"model":[37],"program":[38],"($D$-MMP).":[39],"As":[40],"a":[41,101],"consequence,":[42],"arbitrary":[46],"big":[47,115],"can":[49,144],"be":[50,145],"systematically":[51],"reduced":[52],"to":[53,86,100,127,137],"Euler":[54],"characteristics":[55],"$\u03c7(Y,\\mathcal":[56],"O_Y(D))$":[57],"on":[58,113],"suitable":[59,102],"models":[61],"$Y$":[62],"using":[63],"vanishing":[64],"theorems,":[65],"extending":[66],"classical":[67],"positivity-based":[68],"methods":[69],"beyond":[70],"movable":[72],"cone.":[73,141],"The":[74],"reduction":[75],"proceeds":[76],"removing":[78],"fixed":[79],"divisorial":[80],"components,":[81],"which":[82],"do":[83],"not":[84],"contribute":[85],"space":[88],"sections,":[91],"either":[92],"directly":[93],"subtraction":[95],"or":[96],"birationally":[97],"contraction":[99],"model.":[104],"obtain":[106],"piecewise":[107],"quasipolynomial":[108],"formulae":[109,136,143],"cone,":[116],"whose":[117],"domains":[118],"Mori":[121],"chambers":[122],"$D$-MMP.":[125],"Restricting":[126],"subclass":[129],"Fano":[131],"type":[132],"extends":[134],"such":[135],"entire":[139],"effective":[140],"These":[142],"constructed":[146],"from":[147,170],"just":[148],"small":[150],"class":[152],"$X$,":[154],"yet":[155],"encode":[156],"properties":[157],"all":[159],"contractions":[161],"$X$.":[163],"Alongside":[164],"computation":[166],"geometry,":[172],"we":[173],"study":[174],"inverse":[176],"process,":[177],"wherein":[178],"finite":[179],"computations":[180],"$h^0(X,\\mathcal":[182],"O_X(D))$":[183],"determine":[184],"chamber":[188],"decomposition":[189],"associated":[192],"models.":[194]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
