{"id":"https://openalex.org/W7206199667","doi":"https://doi.org/10.48550/arxiv.2609.00758","title":"Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities","display_name":"Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7206199667","doi":"https://doi.org/10.48550/arxiv.2609.00758"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.00758","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00758","pdf_url":"https://arxiv.org/pdf/2609.00758","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":"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/2609.00758","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080802980","display_name":"Yohsuke Imagi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Imagi, Yohsuke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5080802980"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.7182999849319458,"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":0.7182999849319458,"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":0.2808000147342682,"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":9.999999747378752e-05,"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/calabi-yau-manifolds","display_name":"Calabi-Yau manifolds","score":0.7960000038146973},{"id":"https://openalex.org/keywords/fano-varieties","display_name":"Fano varieties","score":0.9769999980926514},{"id":"https://openalex.org/keywords/isolated-singularities","display_name":"isolated singularities","score":0.9610000252723694},{"id":"https://openalex.org/keywords/log-canonical-singularities","display_name":"log canonical singularities","score":0.7950000166893005},{"id":"https://openalex.org/keywords/kahler-manifolds","display_name":"K\u00e4hler manifolds","score":0.7039999961853027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8019999861717224},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6869000196456909},{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.6589000225067139},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.6438000202178955},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6351000070571899},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.633899986743927},{"id":"https://openalex.org/C143161588","wikidata":"https://www.wikidata.org/wiki/Q906907","display_name":"Coherent sheaf","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C18109118","wikidata":"https://www.wikidata.org/wiki/Q5251702","display_name":"Deformation theory","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32510000467300415},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.00758","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00758","pdf_url":"https://arxiv.org/pdf/2609.00758","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.00758","doi":"https://doi.org/10.48550/arxiv.2609.00758","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.00758","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:2609.00758","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00758","pdf_url":"https://arxiv.org/pdf/2609.00758","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":"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/W7206199667.pdf","grobid_xml":"https://content.openalex.org/works/W7206199667.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4417260795","https://openalex.org/W7077909837","https://openalex.org/W7128520173"],"related_works":["https://openalex.org/W4413344999","https://openalex.org/W4417260795","https://openalex.org/W7128520173","https://openalex.org/W4415978481","https://openalex.org/W4410311948","https://openalex.org/W7098291965","https://openalex.org/W2793266751","https://openalex.org/W2608266330","https://openalex.org/W2136020066","https://openalex.org/W71504133"],"abstract_inverted_index":{"Let":[0],"$X$":[1,28,44,54],"be":[2],"a":[3,24,39,56],"compact":[4],"log-canonical":[5,58],"K\u00e4hler":[6],"$n$-fold,":[7,59],"$n\\ge3,$":[8,60],"with":[9,14,61,66],"trivial":[10],"canonical":[11],"sheaf":[12,64],"and":[13,65,92,95,106],"isolated":[15,67],"singularities.":[16],"We":[17],"prove":[18],"that":[19],"the":[20,35,45,70,76],"generic":[21,46,71],"fibres":[22,47,72],"of":[23,27,82,85,89,99,103,109],"semi-universal":[25],"deformation":[26],"have":[29,48,73],"Du":[30],"Bois":[31],"invariant":[32,51],"$b^{1,n-2}=0$":[33],"at":[34],"singular":[36,90],"points.":[37],"Under":[38],"certain":[40,107],"topological":[41,77],"hypothesis":[42],"on":[43],"also":[49],"link":[50],"$l^{1,n-2}=0.$":[52],"If":[53],"is":[55],"projective":[57],"ample":[62],"anti-canonical":[63],"singularities":[68],"then":[69],"$b^{1,n-2}=l^{1,n-2}=0$":[74],"(without":[75],"hypothesis).":[78],"These":[79],"are":[80],"generalizations":[81],"recent":[83],"results":[84],"Tenie":[86],"`Global":[87],"smoothing":[88],"Fano":[91],"Calabi--Yau":[93,104],"varieties'":[94],"an":[96],"older":[97],"result":[98],"Namikawa":[100],"`Deformation":[101],"theory":[102],"threefolds":[105],"invariants":[108],"singularities.'":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-03T00:00:00"}
