{"id":"https://openalex.org/W7222995270","doi":"https://doi.org/10.48550/arxiv.2610.24134","title":"Invariants of big classes from asymptotic total Betti numbers","display_name":"Invariants of big classes from asymptotic total Betti numbers","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222995270","doi":"https://doi.org/10.48550/arxiv.2610.24134"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.24134","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24134","pdf_url":"https://arxiv.org/pdf/2610.24134","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/2610.24134","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088449176","display_name":"Michele Ancona","orcid":"https://orcid.org/0000-0002-7164-188X","observed_orcids":["https://orcid.org/0000-0002-7164-188X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ancona, Michele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101643442","display_name":"Junyan Cao","orcid":"https://orcid.org/0009-0003-0301-1549","observed_orcids":["https://orcid.org/0009-0003-0301-1549"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cao, Junyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.9951000213623047,"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":0.9951000213623047,"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":0.0031999999191612005,"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":0.000699999975040555,"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/big-line-bundles","display_name":"big line bundles","score":0.9710000157356262},{"id":"https://openalex.org/keywords/hypersurfaces","display_name":"hypersurfaces","score":0.7820000052452087},{"id":"https://openalex.org/keywords/zariski-decomposition","display_name":"Zariski decomposition","score":0.9129999876022339},{"id":"https://openalex.org/keywords/birational-invariants","display_name":"birational invariants","score":0.9470000267028809},{"id":"https://openalex.org/keywords/real-algebraic-hypersurfaces","display_name":"real algebraic hypersurfaces","score":0.8820000290870667},{"id":"https://openalex.org/keywords/asymptotic-geometry","display_name":"asymptotic geometry","score":0.4620000123977661}],"concepts":[{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.9107000231742859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8359000086784363},{"id":"https://openalex.org/C137134375","wikidata":"https://www.wikidata.org/wiki/Q1509762","display_name":"Line bundle","level":2,"score":0.7480000257492065},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6193000078201294},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5879999995231628},{"id":"https://openalex.org/C40926966","wikidata":"https://www.wikidata.org/wiki/Q4748472","display_name":"Ample line bundle","level":2,"score":0.5565000176429749},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.5460000038146973},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5443999767303467},{"id":"https://openalex.org/C62139920","wikidata":"https://www.wikidata.org/wiki/Q3554818","display_name":"Projective variety","level":2,"score":0.49300000071525574},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C21555199","wikidata":"https://www.wikidata.org/wiki/Q5535491","display_name":"Geometric invariant theory","level":5,"score":0.42559999227523804},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.3822999894618988},{"id":"https://openalex.org/C113441369","wikidata":"https://www.wikidata.org/wiki/Q23937546","display_name":"Real projective line","level":5,"score":0.37459999322891235},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C66384103","wikidata":"https://www.wikidata.org/wiki/Q2370925","display_name":"Normal bundle","level":3,"score":0.36320000886917114},{"id":"https://openalex.org/C90685605","wikidata":"https://www.wikidata.org/wiki/Q764115","display_name":"Projective line","level":4,"score":0.32190001010894775},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.31940001249313354},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29499998688697815},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2752000093460083},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.27300000190734863},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.24134","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24134","pdf_url":"https://arxiv.org/pdf/2610.24134","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.2610.24134","doi":"https://doi.org/10.48550/arxiv.2610.24134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.24134","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.24134","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24134","pdf_url":"https://arxiv.org/pdf/2610.24134","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/W7222995270.pdf","grobid_xml":"https://content.openalex.org/works/W7222995270.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1517871693","https://openalex.org/W7126061298"],"related_works":["https://openalex.org/W1517871693","https://openalex.org/W2076581767","https://openalex.org/W2034850154","https://openalex.org/W2802156538","https://openalex.org/W2952860814","https://openalex.org/W3097553073","https://openalex.org/W2089102094","https://openalex.org/W3087760490","https://openalex.org/W2167218575","https://openalex.org/W1966208864"],"abstract_inverted_index":{"We":[0,36,91],"introduce":[1],"and":[2,43],"study":[3],"a":[4,61,88,115],"new":[5],"numerical":[6],"invariant":[7,40,69],"of":[8,20,25,32,51,105,114],"big":[9,57,116],"line":[10,34,53,58,80,117],"bundles":[11],"on":[12,87],"normal":[13],"complex":[14],"projective":[15,89],"varieties,":[16],"defined":[17,86],"in":[18,97],"terms":[19],"the":[21,33,49,52,56,68,72,79,94,98,103],"total":[22,126],"Betti":[23,127],"number":[24],"hypersurfaces":[26,108],"associated":[27,109],"with":[28,71,110],"high":[29,111],"tensor":[30,112],"powers":[31,113],"bundle.":[35,54],"prove":[37],"that":[38,67],"this":[39,76],"is":[41,82,85],"birational":[42],"provides":[44],"an":[45],"upper":[46],"bound":[47],"for":[48],"volume":[50],"When":[55],"bundle":[59,81,118],"admits":[60],"rational":[62],"Zariski":[63],"decomposition,":[64],"we":[65],"show":[66],"coincides":[70],"volume.":[73],"In":[74],"particular,":[75],"holds":[77],"when":[78],"ample":[83],"or":[84],"surface.":[90],"also":[92],"investigate":[93],"analogous":[95],"problem":[96],"real":[99,106,120],"algebraic":[100,107],"setting,":[101],"proving":[102],"existence":[104],"whose":[119],"vanishing":[121],"loci":[122],"have":[123],"arbitrarily":[124],"large":[125],"numbers.":[128]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}