{"id":"https://openalex.org/W7212002914","doi":"https://doi.org/10.48550/arxiv.2609.06683","title":"Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory","display_name":"Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory","publication_year":2026,"publication_date":"2026-09-06","ids":{"openalex":"https://openalex.org/W7212002914","doi":"https://doi.org/10.48550/arxiv.2609.06683"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06683","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06683","pdf_url":"https://arxiv.org/pdf/2609.06683","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/2609.06683","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138398084","display_name":"Jie Fu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Jie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5150900177","display_name":"Zhiwei Zheng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Zhiwei","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":2,"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":0.9994999766349792,"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":0.9994999766349792,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.00019999999494757503,"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"}},{"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/automorphism-groups","display_name":"automorphism groups","score":0.8629999756813049},{"id":"https://openalex.org/keywords/period-map","display_name":"period map","score":0.6869999766349792},{"id":"https://openalex.org/keywords/lattice-theory","display_name":"lattice theory","score":0.6809999942779541},{"id":"https://openalex.org/keywords/lattice-enumeration","display_name":"lattice enumeration","score":0.574999988079071},{"id":"https://openalex.org/keywords/k3-surfaces","display_name":"K3 surfaces","score":0.46799999475479126},{"id":"https://openalex.org/keywords/hodge-structures","display_name":"Hodge structures","score":0.45500001311302185}],"concepts":[{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.8680999875068665},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7386000156402588},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.6744999885559082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6597999930381775},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5548999905586243},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5273000001907349},{"id":"https://openalex.org/C7619685","wikidata":"https://www.wikidata.org/wiki/Q3630548","display_name":"Outer automorphism group","level":4,"score":0.4408999979496002},{"id":"https://openalex.org/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.39169999957084656},{"id":"https://openalex.org/C168025344","wikidata":"https://www.wikidata.org/wiki/Q7391963","display_name":"SO(8)","level":5,"score":0.38580000400543213},{"id":"https://openalex.org/C91429207","wikidata":"https://www.wikidata.org/wiki/Q5192245","display_name":"Cubic form","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29670000076293945}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06683","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06683","pdf_url":"https://arxiv.org/pdf/2609.06683","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.2609.06683","doi":"https://doi.org/10.48550/arxiv.2609.06683","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06683","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:2609.06683","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06683","pdf_url":"https://arxiv.org/pdf/2609.06683","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/W7212002914.pdf","grobid_xml":"https://content.openalex.org/works/W7212002914.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7084040373","https://openalex.org/W7164323481"],"related_works":["https://openalex.org/W3193368955","https://openalex.org/W7164323481","https://openalex.org/W7213579051","https://openalex.org/W7222168086","https://openalex.org/W7126262913","https://openalex.org/W4410630174","https://openalex.org/W4411393851","https://openalex.org/W7084040373","https://openalex.org/W4402903719","https://openalex.org/W1532725039"],"abstract_inverted_index":{"Laza":[0],"and":[1,21,74],"the":[2,43,64],"second":[3],"author":[4],"have":[5],"classified":[6],"all":[7,46],"possible":[8,47],"symplectic":[9,33],"automorphism":[10,34,48],"groups":[11],"of":[12,28,45,52,67],"smooth":[13],"cubic":[14,29,68],"fourfolds.":[15],"There":[16],"are":[17,25],"$34$":[18],"such":[19],"groups,":[20],"by":[22,70],"Koike,":[23],"there":[24],"$48$":[26],"families":[27],"fourfolds":[30,69],"with":[31],"speficied":[32],"group.":[35],"For":[36],"$42$":[37],"among":[38],"those":[39],"families,":[40],"we":[41],"complete":[42],"classification":[44],"groups.":[49],"The":[50],"approach":[51],"this":[53],"paper":[54],"is":[55],"mainly":[56],"lattice":[57],"theoretic,":[58],"starting":[59],"from":[60],"known":[61],"results":[62],"about":[63],"period":[65],"map":[66],"Voisin,":[71],"Hassett,":[72],"Looijenga":[73],"Laza.":[75],"We":[76],"use":[77],"a":[78],"lattice-enumeration":[79],"algorithm":[80],"implemented":[81],"in":[82],"OSCAR.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}