{"id":"https://openalex.org/W7220729812","doi":"https://doi.org/10.48550/arxiv.2610.05795","title":"Instability of the Fundamental Group for Ricci-Flat K\u00e4hler 4-Manifolds","display_name":"Instability of the Fundamental Group for Ricci-Flat K\u00e4hler 4-Manifolds","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220729812","doi":"https://doi.org/10.48550/arxiv.2610.05795"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05795","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05795","pdf_url":"https://arxiv.org/pdf/2610.05795","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/2610.05795","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003895232","display_name":"Alejandro Bellati","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bellati, Alejandro","raw_affiliation_strings":["Department of Mathematics , Princeton University , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Princeton University , USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085486133","display_name":"Ignacio Bustamante","orcid":"https://orcid.org/0000-0002-8305-8106","observed_orcids":["https://orcid.org/0000-0002-8305-8106"]},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Bustamante, Ignacio","raw_affiliation_strings":["IMERL , Universidad de la Rep\u00fablica , Uruguay"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMERL , Universidad de la Rep\u00fablica , Uruguay","institution_ids":["https://openalex.org/I180910786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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":0.9907000064849854,"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":0.9907000064849854,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.007000000216066837,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.00139999995008111,"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/fundamental-group","display_name":"fundamental group","score":0.6439999938011169},{"id":"https://openalex.org/keywords/ricci-flat-kahler-metrics","display_name":"Ricci-flat K\u00e4hler metrics","score":0.7950000166893005},{"id":"https://openalex.org/keywords/k3-surfaces","display_name":"K3 surfaces","score":0.6809999942779541},{"id":"https://openalex.org/keywords/enriques-surfaces","display_name":"Enriques surfaces","score":1.0},{"id":"https://openalex.org/keywords/ricci-flow","display_name":"Ricci flow","score":0.48399999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6884999871253967},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6614999771118164},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.6060000061988831},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.572700023651123},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5494999885559082},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.47699999809265137},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.474700003862381},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38589999079704285},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.3440999984741211},{"id":"https://openalex.org/C58450382","wikidata":"https://www.wikidata.org/wiki/Q2147620","display_name":"Locally compact group","level":3,"score":0.3073999881744385},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2775000035762787},{"id":"https://openalex.org/C10513763","wikidata":"https://www.wikidata.org/wiki/Q1331774","display_name":"Fundamental frequency","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2621000111103058}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05795","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05795","pdf_url":"https://arxiv.org/pdf/2610.05795","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.2610.05795","doi":"https://doi.org/10.48550/arxiv.2610.05795","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05795","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:2610.05795","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05795","pdf_url":"https://arxiv.org/pdf/2610.05795","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220729812.pdf","grobid_xml":"https://content.openalex.org/works/W7220729812.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W5113826","https://openalex.org/W1512537105","https://openalex.org/W1532335958","https://openalex.org/W1547847658","https://openalex.org/W1608729807","https://openalex.org/W1949785703","https://openalex.org/W1992432286","https://openalex.org/W1993403739","https://openalex.org/W1994007445","https://openalex.org/W2005727105","https://openalex.org/W2013097258","https://openalex.org/W2026429431","https://openalex.org/W2027673210","https://openalex.org/W2028338587","https://openalex.org/W2039948096","https://openalex.org/W2055401035","https://openalex.org/W2061658404","https://openalex.org/W2075114146","https://openalex.org/W2078812735","https://openalex.org/W2078817916","https://openalex.org/W2081028496","https://openalex.org/W2088494056","https://openalex.org/W2138564812","https://openalex.org/W2976792280","https://openalex.org/W3164420100","https://openalex.org/W4367394048","https://openalex.org/W4394660448","https://openalex.org/W4406460081","https://openalex.org/W4409001768","https://openalex.org/W4417466864","https://openalex.org/W7117313006","https://openalex.org/W7120218310"],"related_works":["https://openalex.org/W6979291654","https://openalex.org/W7125121455","https://openalex.org/W4410105186","https://openalex.org/W2951854291","https://openalex.org/W2130378201","https://openalex.org/W2746137899","https://openalex.org/W7099410461","https://openalex.org/W2475282434","https://openalex.org/W3201885494","https://openalex.org/W3147494517"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,35],"the":[3,38,44,71],"fundamental":[4,59],"group":[5],"is":[6],"not":[7],"locally":[8,54],"stable":[9],"under":[10],"non-collapsed":[11],"Gromov--Hausdorff":[12],"convergence,":[13],"even":[14],"among":[15],"closed":[16,53],"Ricci-flat":[17,26,56],"K\u00e4hler":[18,27],"four-manifolds.":[19],"More":[20],"precisely,":[21],"we":[22,47],"construct":[23,49],"families":[24,51],"of":[25,52],"metrics":[28],"on":[29],"$K3$":[30],"surfaces":[31,34],"and":[32,63],"Enriques":[33],"converge":[36,69],"to":[37,70],"same":[39,45,72],"compact":[40,73],"flat":[41,74],"orbifold.":[42,75],"Using":[43],"mechanism,":[46],"further":[48],"two":[50],"hyperk\u00e4hler":[55],"four-manifolds,":[57],"with":[58],"groups":[60],"$\\mathbb":[61,64],"Z_2$":[62],"Z_2\\times\\mathbb":[65],"Z_2$,":[66],"respectively,":[67],"which":[68]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
