{"id":"https://openalex.org/W7213238558","doi":"https://doi.org/10.48550/arxiv.2609.14435","title":"Deformation invariance of canonical nefness in smooth Kahler morphisms","display_name":"Deformation invariance of canonical nefness in smooth Kahler morphisms","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213238558","doi":"https://doi.org/10.48550/arxiv.2609.14435"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14435","pdf_url":"https://arxiv.org/pdf/2609.14435","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.14435","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134896569","display_name":"Mu-Lin Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Mu-Lin","raw_affiliation_strings":["School of Mathematics , Hunan University , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hunan University , China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040713510","display_name":"Xiao-Lei Liu","orcid":"https://orcid.org/0000-0002-4279-9231","observed_orcids":["https://orcid.org/0000-0002-4279-9231"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xiao-Lei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017443527","display_name":"Sheng Rao","orcid":"https://orcid.org/0000-0003-4203-3540","observed_orcids":["https://orcid.org/0000-0003-4203-3540"]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rao, Sheng","raw_affiliation_strings":["School of Mathematics , Hunan University , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hunan University , China","institution_ids":["https://openalex.org/I16609230"]}]}],"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/T12351","display_name":"Geometry and complex manifolds","score":0.8999000191688538,"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/T12351","display_name":"Geometry and complex manifolds","score":0.8999000191688538,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.09969999641180038,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nef-line-bundles","display_name":"nef line bundles","score":0.6740000247955322},{"id":"https://openalex.org/keywords/canonical-bundle","display_name":"canonical bundle","score":0.8450000286102295},{"id":"https://openalex.org/keywords/deformation-invariance","display_name":"deformation invariance","score":0.8510000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7663999795913696},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.7580000162124634},{"id":"https://openalex.org/C2780399754","wikidata":"https://www.wikidata.org/wiki/Q844128","display_name":"Canonical bundle","level":2,"score":0.6926000118255615},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5515999794006348},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.550000011920929},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.5454000234603882},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5407000184059143},{"id":"https://openalex.org/C146710177","wikidata":"https://www.wikidata.org/wiki/Q1154996","display_name":"Fiber bundle","level":3,"score":0.49869999289512634},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.47780001163482666},{"id":"https://openalex.org/C191961195","wikidata":"https://www.wikidata.org/wiki/Q5477902","display_name":"Frame bundle","level":4,"score":0.4235999882221222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40720000863075256},{"id":"https://openalex.org/C519885992","wikidata":"https://www.wikidata.org/wiki/Q161","display_name":"Fiber","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C27602778","wikidata":"https://www.wikidata.org/wiki/Q578874","display_name":"Complex manifold","level":3,"score":0.34850001335144043},{"id":"https://openalex.org/C66384103","wikidata":"https://www.wikidata.org/wiki/Q2370925","display_name":"Normal bundle","level":3,"score":0.34439998865127563},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27239999175071716},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C18109118","wikidata":"https://www.wikidata.org/wiki/Q5251702","display_name":"Deformation theory","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C157135747","wikidata":"https://www.wikidata.org/wiki/Q1353916","display_name":"K\u00e4hler manifold","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14435","pdf_url":"https://arxiv.org/pdf/2609.14435","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.2609.14435","doi":"https://doi.org/10.48550/arxiv.2609.14435","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14435","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.14435","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14435","pdf_url":"https://arxiv.org/pdf/2609.14435","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":[{"id":"https://openalex.org/G1563298894","display_name":null,"funder_award_id":"W2441003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3414394961","display_name":null,"funder_award_id":"12271073","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G500947340","display_name":null,"funder_award_id":"12271412","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213238558.pdf","grobid_xml":"https://content.openalex.org/works/W7213238558.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7213528003","https://openalex.org/W7102394187","https://openalex.org/W2963242853","https://openalex.org/W7100170351","https://openalex.org/W2287662312","https://openalex.org/W4416324406","https://openalex.org/W2250441775","https://openalex.org/W2276779061","https://openalex.org/W4249297937","https://openalex.org/W2613305535"],"abstract_inverted_index":{"Let":[0],"$f\\colon":[1],"X\\to\u0394$":[2],"be":[3],"a":[4],"smooth":[5],"K\u00e4hler":[6,45],"morphism":[7],"from":[8],"complex":[9],"manifold":[10],"$X$":[11],"to":[12],"the":[13,19,44,47,53],"unit":[14],"disc.":[15],"We":[16],"prove":[17],"that":[18],"canonical":[20,54],"bundle":[21,55],"$K_{X_t}$":[22],"is":[23,32],"nef":[24,33],"for":[25,34,50],"\\emph{every}":[26],"fiber":[27],"as":[28,30],"soon":[29],"it":[31],"\\emph{one}":[35],"fiber.":[36],"This":[37],"answers,":[38],"in":[39,43],"arbitrary":[40],"dimension":[41],"and":[42,59],"setting,":[46],"deformation-openness":[48],"problem":[49],"non-nefness":[51],"of":[52],"raised":[56],"by":[57],"Campana":[58],"Peternell.":[60]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-16T00:00:00"}
