{"id":"https://openalex.org/W7221816588","doi":"https://doi.org/10.48550/arxiv.2610.17985","title":"Cohomology ring of the strata of holomorphic differentials of genus 3","display_name":"Cohomology ring of the strata of holomorphic differentials of genus 3","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7221816588","doi":"https://doi.org/10.48550/arxiv.2610.17985"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.17985","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17985","pdf_url":"https://arxiv.org/pdf/2610.17985","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.17985","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122226226","display_name":"Prabhat Devkota","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Devkota, Prabhat","raw_affiliation_strings":["Institut f\u00fcr Mathematik , Goethe-Universit\u00e4t Frankfurt , Robert-Mayer-Stra\u00dfe 6-8 , Frank- furt am Main , 60325 Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik , Goethe-Universit\u00e4t Frankfurt , Robert-Mayer-Stra\u00dfe 6-8 , Frank- furt am Main , 60325 Germany","institution_ids":["https://openalex.org/I114090438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5120867589","display_name":"Myeongjae Lee","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]},{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]},{"id":"https://openalex.org/I592451","display_name":"Indiana University","ror":"https://ror.org/01kg8sb98","country_code":"US","type":"education","lineage":["https://openalex.org/I592451"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Lee, Myeongjae","raw_affiliation_strings":["Department of Mathematics , Indiana University , 831 E. Third Street , Bloomington , IN 47405 , USA","Institut f\u00fcr Mathematik , Goethe-Universit\u00e4t Frankfurt , Robert-Mayer-Stra\u00dfe 6-8 , Frank- furt am Main , 60325 Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Indiana University , 831 E. Third Street , Bloomington , IN 47405 , USA","institution_ids":["https://openalex.org/I4210119109","https://openalex.org/I592451"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik , Goethe-Universit\u00e4t Frankfurt , Robert-Mayer-Stra\u00dfe 6-8 , Frank- furt am Main , 60325 Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":0.9907000064849854,"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/T10061","display_name":"Algebraic Geometry and Number Theory","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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/holomorphic-differentials","display_name":"holomorphic differentials","score":0.8840000033378601},{"id":"https://openalex.org/keywords/genus-3","display_name":"genus 3","score":0.6909999847412109},{"id":"https://openalex.org/keywords/cohomology-ring","display_name":"cohomology ring","score":0.8090000152587891},{"id":"https://openalex.org/keywords/boundary-strata","display_name":"boundary strata","score":0.9240000247955322},{"id":"https://openalex.org/keywords/cycle-class-map","display_name":"cycle class map","score":0.6359999775886536}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8187000155448914},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.7876999974250793},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.7243000268936157},{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.6833999752998352},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6315000057220459},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5687999725341797},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.48510000109672546},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.4602999985218048},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.32760000228881836},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3172000050544739},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.3151000142097473},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.274399995803833},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C45237699","wikidata":"https://www.wikidata.org/wiki/Q1038716","display_name":"Identity theorem","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.17985","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17985","pdf_url":"https://arxiv.org/pdf/2610.17985","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.2610.17985","doi":"https://doi.org/10.48550/arxiv.2610.17985","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.17985","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:2610.17985","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17985","pdf_url":"https://arxiv.org/pdf/2610.17985","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/W7221816588.pdf","grobid_xml":"https://content.openalex.org/works/W7221816588.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7127326470","https://openalex.org/W7131859426","https://openalex.org/W4405289854","https://openalex.org/W4416014886","https://openalex.org/W4361019514","https://openalex.org/W4365452056","https://openalex.org/W2797819706","https://openalex.org/W7162577558","https://openalex.org/W4416014068","https://openalex.org/W4399304950"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"the":[3,12,16,39,44,66,74],"rational":[4,67,79],"Chow":[5],"ring":[6],"of":[7,11,15,35,38,51],"every":[8],"connected":[9],"component":[10],"multi-scale":[13,40],"compactifications":[14,75],"genus":[17],"three":[18],"strata":[19,37,50],"$\\mathcal{H}(4),":[20],"\\mathcal{H}(2,2)$":[21],"and":[22,60,73],"$\\mathcal{H}(3,1)$":[23],"is":[24,70],"generated":[25],"by":[26,42],"boundary-stratum":[27],"classes.":[28],"Our":[29],"proof":[30],"shows":[31],"Chow-K\u00fcnneth":[32],"generation":[33],"property":[34],"boundary":[36,45],"compactification":[41],"reducing":[43],"analysis":[46],"to":[47],"lower-genus":[48],"generalized":[49],"meromorphic":[52],"differentials,":[53],"including":[54],"residueless":[55],"loci,":[56],"described":[57],"through":[58],"plane-quartic":[59],"plane-cubic":[61],"models.":[62],"As":[63],"a":[64],"consequence,":[65],"cycle-class":[68],"map":[69],"an":[71],"isomorphism":[72],"have":[76],"no":[77],"odd":[78],"cohomology.":[80]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-15T00:00:00"}