{"id":"https://openalex.org/W7213528957","doi":"https://doi.org/10.48550/arxiv.2609.18921","title":"Bertini's theorem for $F$-rationality is false","display_name":"Bertini's theorem for $F$-rationality is false","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213528957","doi":"https://doi.org/10.48550/arxiv.2609.18921"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18921","pdf_url":"https://arxiv.org/pdf/2609.18921","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/2609.18921","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015360975","display_name":"Thomas Polstra","orcid":"https://orcid.org/0000-0003-0856-9296","observed_orcids":["https://orcid.org/0000-0003-0856-9296"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Polstra, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035871314","display_name":"Austyn Simpson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simpson, Austyn","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":0.9990000128746033,"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":0.9990000128746033,"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":0.00039999998989515007,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":9.999999747378752e-05,"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/positive-characteristic","display_name":"positive characteristic","score":0.6600000262260437},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.5270000100135803},{"id":"https://openalex.org/keywords/hyperplane-sections","display_name":"hyperplane sections","score":0.7009999752044678},{"id":"https://openalex.org/keywords/affine-varieties","display_name":"affine varieties","score":0.7229999899864197},{"id":"https://openalex.org/keywords/projective-varieties","display_name":"projective varieties","score":0.9769999980926514}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7638000249862671},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.7383999824523926},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6796000003814697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6714000105857849},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6621000170707703},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4893999993801117},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C62139920","wikidata":"https://www.wikidata.org/wiki/Q3554818","display_name":"Projective variety","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3343999981880188},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3140000104904175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2879999876022339},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2768999934196472},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18921","pdf_url":"https://arxiv.org/pdf/2609.18921","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.2609.18921","doi":"https://doi.org/10.48550/arxiv.2609.18921","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18921","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:2609.18921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18921","pdf_url":"https://arxiv.org/pdf/2609.18921","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/G7754679596","display_name":"Algebraic and Geometric Properties of Multiplicities and the Frobenius Endomorphism","funder_award_id":"2502317","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213528957.pdf","grobid_xml":"https://content.openalex.org/works/W7213528957.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415337279","https://openalex.org/W7165614757","https://openalex.org/W2008909306","https://openalex.org/W4399498494","https://openalex.org/W2020707468","https://openalex.org/W87231765","https://openalex.org/W2137304310","https://openalex.org/W7214898521","https://openalex.org/W7154459326","https://openalex.org/W2026161444"],"abstract_inverted_index":{"Let":[0],"$k=\\overline{\\mathbb{F}_2}$.":[1],"We":[2,39],"construct":[3,41],"a":[4,11,19,42,49],"nine-dimensional":[5,43],"$F$-rational":[6,31,45],"affine":[7],"variety":[8,46],"$X$":[9],"admitting":[10],"locally":[12],"closed":[13,50],"embedding":[14,51],"$X\\hookrightarrow":[15],"\\mathbb{P}_k^{19}$":[16],"together":[17],"with":[18],"dense":[20],"open":[21],"set":[22],"$U\\subseteq":[23],"(\\mathbb{P}^{19})^\\vee$":[24],"such":[25],"that":[26],"$X\\cap":[27],"H$":[28],"is":[29],"not":[30],"(or":[32],"even":[33],"$F$-injective)":[34],"for":[35],"all":[36],"$H\\in":[37],"U$.":[38],"also":[40],"projective":[44],"$\\mathfrak{X}$":[47],"and":[48],"$\\mathfrak{X}\\hookrightarrow\\mathbb{P}^{29}_k$":[52],"under":[53],"which":[54],"the":[55],"same":[56],"conclusion":[57],"holds.":[58]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-18T00:00:00"}
