{"id":"https://openalex.org/W7215752123","doi":"https://doi.org/10.48550/arxiv.2610.00378","title":"Stratification of Joint Moduli Spaces of Higgs Bundles","display_name":"Stratification of Joint Moduli Spaces of Higgs Bundles","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7215752123","doi":"https://doi.org/10.48550/arxiv.2610.00378"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00378","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00378","pdf_url":"https://arxiv.org/pdf/2610.00378","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/2610.00378","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123505691","display_name":"Shiyu Cao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cao, Shiyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5123505691"],"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":0.6176999807357788,"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":0.6176999807357788,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.3127000033855438,"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":0.031099999323487282,"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/higgs-bundles","display_name":"Higgs bundles","score":0.9860000014305115},{"id":"https://openalex.org/keywords/moduli-spaces","display_name":"moduli spaces","score":0.699999988079071},{"id":"https://openalex.org/keywords/teichmuller-space","display_name":"Teichm\u00fcller space","score":0.8799999952316284},{"id":"https://openalex.org/keywords/whitney-stratification","display_name":"Whitney stratification","score":0.7250000238418579},{"id":"https://openalex.org/keywords/poisson-brackets","display_name":"Poisson brackets","score":0.8069999814033508},{"id":"https://openalex.org/keywords/kobayashi-hitchin-correspondence","display_name":"Kobayashi-Hitchin correspondence","score":0.8999999761581421},{"id":"https://openalex.org/keywords/hyperkahler-structures","display_name":"hyperk\u00e4hler structures","score":0.9039999842643738},{"id":"https://openalex.org/keywords/holomorphic-submersions","display_name":"holomorphic submersions","score":0.7760000228881836}],"concepts":[{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.8888999819755554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7764000296592712},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.7232999801635742},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7128000259399414},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.5809000134468079},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5720999836921692},{"id":"https://openalex.org/C197375991","wikidata":"https://www.wikidata.org/wiki/Q1464936","display_name":"Poisson manifold","level":3,"score":0.5446000099182129},{"id":"https://openalex.org/C188845816","wikidata":"https://www.wikidata.org/wiki/Q1052775","display_name":"Poisson bracket","level":3,"score":0.48649999499320984},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.46720001101493835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4083000123500824},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C104367098","wikidata":"https://www.wikidata.org/wiki/Q5454146","display_name":"First class constraint","level":5,"score":0.37869998812675476},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3546000123023987},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.3206999897956848},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.3111000061035156},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2953000068664551},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C88324339","wikidata":"https://www.wikidata.org/wiki/Q2103196","display_name":"Polydisc","level":3,"score":0.2939999997615814},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.27300000190734863},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C133769200","wikidata":"https://www.wikidata.org/wiki/Q174565","display_name":"Bracket","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C125849494","wikidata":"https://www.wikidata.org/wiki/Q766774","display_name":"Symplectic vector space","level":5,"score":0.26030001044273376},{"id":"https://openalex.org/C27602778","wikidata":"https://www.wikidata.org/wiki/Q578874","display_name":"Complex manifold","level":3,"score":0.2549999952316284},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00378","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00378","pdf_url":"https://arxiv.org/pdf/2610.00378","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.2610.00378","doi":"https://doi.org/10.48550/arxiv.2610.00378","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00378","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:2610.00378","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00378","pdf_url":"https://arxiv.org/pdf/2610.00378","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/W7215752123.pdf","grobid_xml":"https://content.openalex.org/works/W7215752123.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1571072992","https://openalex.org/W1575147392","https://openalex.org/W2060663265","https://openalex.org/W2083377513","https://openalex.org/W3090146839","https://openalex.org/W3106710573","https://openalex.org/W3193204122","https://openalex.org/W4248532778","https://openalex.org/W4321640306","https://openalex.org/W7111034054","https://openalex.org/W7170046089","https://openalex.org/W7214077028"],"related_works":["https://openalex.org/W3193204122","https://openalex.org/W3184350511","https://openalex.org/W7214077028","https://openalex.org/W3016134739","https://openalex.org/W2766009877","https://openalex.org/W2232714323","https://openalex.org/W4223430533","https://openalex.org/W2477721195","https://openalex.org/W2766207158","https://openalex.org/W6920831763"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,19,24,63,71,76,81,104,107],"marked":[3],"analytic":[4],"moduli":[5],"space":[6,37],"of":[7,18,106],"polystable":[8],"degree-zero":[9],"$\\mathrm{SL}_r(\\C)$-Higgs":[10],"bundles":[11],"over":[12],"Teichm\u00fcller":[13,36],"space.":[14,109],"The":[15,33,94],"connected":[16,72],"components":[17],"orbit-type":[20,73],"loci":[21],"defined":[22],"by":[23],"full":[25],"determinant-one":[26],"stabilizers":[27],"form":[28],"a":[29,39,48,57],"complex":[30],"Whitney":[31],"stratification.":[32],"projection":[34],"to":[35],"is":[38,84],"holomorphic":[40,51,59],"submersion":[41],"on":[42,62,86],"every":[43,87],"stratum.":[44],"Each":[45],"stratum":[46,88],"carries":[47],"canonical":[49],"relative":[50],"symplectic":[52,68],"form.":[53],"These":[54],"forms":[55],"determine":[56],"vertical":[58,98],"Poisson":[60],"bracket":[61],"reduced":[64],"structure":[65],"sheaf,":[66],"whose":[67],"leaves":[69],"are":[70],"strata":[74,105],"in":[75],"fibers.":[77],"On":[78],"each":[79],"fiber,":[80],"Hitchin--Kobayashi":[82],"correspondence":[83],"biholomorphic":[85],"and":[89,97],"identifies":[90],"its":[91],"hyperk\u00e4hler":[92,99],"structure.":[93],"harmonic":[95],"representatives":[96],"tensors":[100],"vary":[101],"smoothly":[102],"along":[103],"total":[108]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}
