{"id":"https://openalex.org/W7214729314","doi":"https://doi.org/10.48550/arxiv.2609.33537","title":"On the algebraicity of non-abelian Noether-Lefschetz loci of rank-two real local systems","display_name":"On the algebraicity of non-abelian Noether-Lefschetz loci of rank-two real local systems","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214729314","doi":"https://doi.org/10.48550/arxiv.2609.33537"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33537","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33537","pdf_url":"https://arxiv.org/pdf/2609.33537","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/2609.33537","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138014056","display_name":"Tianzhi Hu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Tianzhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137963904","display_name":"Kang Zuo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuo, Kang","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":0.9018999934196472,"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":0.9018999934196472,"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":0.07429999858140945,"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":0.013500000350177288,"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/algebraicity","display_name":"algebraicity","score":0.6669999957084656},{"id":"https://openalex.org/keywords/non-unitary-representations","display_name":"non-unitary representations","score":0.621999979019165},{"id":"https://openalex.org/keywords/sl-2-r","display_name":"SL(2,R)","score":0.5619999766349792},{"id":"https://openalex.org/keywords/period-map","display_name":"period map","score":0.578000009059906},{"id":"https://openalex.org/keywords/moduli-space-of-curves","display_name":"moduli space of curves","score":0.7960000038146973}],"concepts":[{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.929099977016449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7455000281333923},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5667999982833862},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5286999940872192},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.5008999705314636},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4799000024795532},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.42559999227523804},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.39879998564720154},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3801000118255615},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31790000200271606},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.30970001220703125},{"id":"https://openalex.org/C2780311589","wikidata":"https://www.wikidata.org/wiki/Q6901559","display_name":"Monodromy matrix","level":3,"score":0.30550000071525574},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25369998812675476},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33537","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33537","pdf_url":"https://arxiv.org/pdf/2609.33537","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.2609.33537","doi":"https://doi.org/10.48550/arxiv.2609.33537","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33537","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:2609.33537","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33537","pdf_url":"https://arxiv.org/pdf/2609.33537","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214729314.pdf","grobid_xml":"https://content.openalex.org/works/W7214729314.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4415054945","https://openalex.org/W7111034054","https://openalex.org/W7116118297","https://openalex.org/W7165188589","https://openalex.org/W7172539026"],"related_works":["https://openalex.org/W7163694607","https://openalex.org/W7099753655","https://openalex.org/W7037952232","https://openalex.org/W4367701265","https://openalex.org/W7214204932","https://openalex.org/W1970301502","https://openalex.org/W6888044416","https://openalex.org/W7095978731","https://openalex.org/W3152733621","https://openalex.org/W2108953739"],"abstract_inverted_index":{"As":[0,83],"a":[1,37,47,58,77,120],"non-abelian":[2,11,60],"analogue":[3],"of":[4,32,50,57,67,122],"the":[5,10,29,73],"Hodge":[6],"locus,":[7],"Simpson":[8],"introduced":[9],"Noether--Lefschetz":[12,61,100],"locus":[13],"and":[14,69,98,102],"conjectured":[15],"its":[16],"algebraicity":[17,56],"for":[18],"$\\mathbb":[19,48,125],"Z$PVHS.":[20],"In":[21],"this":[22,26,71],"paper,":[23],"we":[24,53,85],"study":[25],"question":[27,121],"on":[28],"moduli":[30],"space":[31],"curves":[33],"$\\mathcal":[34],"M_g$.":[35],"For":[36],"non-unitary":[38],"representation":[39],"\\[":[40],"\u03c1:\u03c0_1(\u03a3_g)\\longrightarrow":[41],"\\mathrm{SL}_2(\\mathbb":[42],"R)":[43],"\\]":[44],"which":[45],"admits":[46],"R$PVHS":[49],"weight":[51],"one,":[52],"prove":[54],"that":[55],"positive-dimensional":[59],"component":[62,74],"is":[63,75,110],"equivalent":[64],"to":[65,119],"discreteness":[66],"$\\operatorname{im}\u03c1$,":[68],"in":[70],"case":[72],"precisely":[76],"marked":[78],"fixed-target":[79],"orbifold":[80],"Hurwitz":[81],"component.":[82],"applications,":[84],"construct":[86],"two":[87],"explicit":[88],"rational":[89],"families":[90],"by":[91],"slit":[92],"surgery:":[93],"one":[94],"with":[95,104],"non-discrete":[96],"monodromy":[97,106],"non-algebraic":[99],"image,":[101],"another":[103],"discrete":[105],"whose":[107],"period":[108],"map":[109],"nevertheless":[111],"non-uniformizing.":[112],"The":[113],"latter":[114],"gives":[115],"an":[116],"affirmative":[117],"answer":[118],"Baldi--Lam":[123],"concerning":[124],"Q$PVHS.":[126]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
