{"id":"https://openalex.org/W7213106207","doi":"https://doi.org/10.48550/arxiv.2609.13025","title":"Positivity properties of Schur classes","display_name":"Positivity properties of Schur classes","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7213106207","doi":"https://doi.org/10.48550/arxiv.2609.13025"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13025","pdf_url":"https://arxiv.org/pdf/2609.13025","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/2609.13025","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073686311","display_name":"Matt Larson","orcid":"https://orcid.org/0000-0002-0852-7881","observed_orcids":["https://orcid.org/0000-0002-0852-7881"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Larson, Matt","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016209997","display_name":"Alan Stapledon","orcid":"https://orcid.org/0009-0000-4381-4942","observed_orcids":["https://orcid.org/0009-0000-4381-4942"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stapledon, Alan","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":1,"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":0.8651999831199646,"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":0.8651999831199646,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.11150000244379044,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.006800000090152025,"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/schur-class","display_name":"Schur class","score":0.9990000128746033},{"id":"https://openalex.org/keywords/positivity","display_name":"positivity","score":0.5619999766349792},{"id":"https://openalex.org/keywords/ample-vector-bundles","display_name":"ample vector bundles","score":0.9350000023841858},{"id":"https://openalex.org/keywords/hodge-riemann-relations","display_name":"Hodge-Riemann relations","score":0.9959999918937683},{"id":"https://openalex.org/keywords/matroids","display_name":"matroid theory","score":0.8730000257492065},{"id":"https://openalex.org/keywords/nonnegativity","display_name":"nonnegativity","score":0.5910000205039978}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8130999803543091},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.579200029373169},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.486299991607666},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.46000000834465027},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.4587000012397766},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C56907000","wikidata":"https://www.wikidata.org/wiki/Q1365548","display_name":"Principal bundle","level":3,"score":0.40799999237060547},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C144947467","wikidata":"https://www.wikidata.org/wiki/Q2397465","display_name":"Tautological line bundle","level":5,"score":0.3540000021457672},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.3179999887943268},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3084000051021576},{"id":"https://openalex.org/C29701004","wikidata":"https://www.wikidata.org/wiki/Q1786292","display_name":"Schur's theorem","level":5,"score":0.3019999861717224},{"id":"https://openalex.org/C62139920","wikidata":"https://www.wikidata.org/wiki/Q3554818","display_name":"Projective variety","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C102591085","wikidata":"https://www.wikidata.org/wiki/Q17103152","display_name":"Schur product theorem","level":5,"score":0.28519999980926514},{"id":"https://openalex.org/C132702353","wikidata":"https://www.wikidata.org/wiki/Q2538404","display_name":"Complex projective space","level":4,"score":0.2842999994754791},{"id":"https://openalex.org/C137134375","wikidata":"https://www.wikidata.org/wiki/Q1509762","display_name":"Line bundle","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.26269999146461487},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26260000467300415},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C100220837","wikidata":"https://www.wikidata.org/wiki/Q2997419","display_name":"Projective linear group","level":5,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13025","pdf_url":"https://arxiv.org/pdf/2609.13025","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.2609.13025","doi":"https://doi.org/10.48550/arxiv.2609.13025","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13025","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:2609.13025","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13025","pdf_url":"https://arxiv.org/pdf/2609.13025","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/W7213106207.pdf","grobid_xml":"https://content.openalex.org/works/W7213106207.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2940556565","https://openalex.org/W4399554736","https://openalex.org/W4405470381","https://openalex.org/W4416020951","https://openalex.org/W4416438496","https://openalex.org/W7104043096","https://openalex.org/W7155492633"],"related_works":["https://openalex.org/W3206216807","https://openalex.org/W2947558102","https://openalex.org/W3176218143","https://openalex.org/W2105552465","https://openalex.org/W7155492633","https://openalex.org/W2074662969","https://openalex.org/W7123629773","https://openalex.org/W2963498174","https://openalex.org/W4414973998","https://openalex.org/W2039313259"],"abstract_inverted_index":{"Results":[0],"of":[1,9,43,71,83,103],"Fulton-Lazarsfeld":[2],"and":[3,11],"Ross-Toma":[4],"show":[5,29],"that":[6,30,100],"Schur":[7,66,101],"classes":[8,67],"ample":[10,85],"nef":[12],"vector":[13,86],"bundles":[14],"have":[15],"remarkable":[16],"positivity":[17],"properties.":[18],"We":[19,28,94],"generalize":[20],"these":[21],"results":[22],"to":[23,59,98],"a":[24,32,36,44,48,60,69,89],"purely":[25],"algebraic":[26],"setting.":[27],"if":[31],"projective":[33,45,51,92],"bundle":[34,46,87],"ring,":[35],"ring":[37,42],"which":[38],"resembles":[39],"the":[40,54,64,72,81],"cohomology":[41],"over":[47,88],"smooth":[49,90],"complex":[50,91],"variety,":[52],"has":[53],"K\u00e4hler":[55],"package":[56],"with":[57],"respect":[58],"suitable":[61],"cone,":[62],"then":[63],"associated":[65],"satisfy":[68],"version":[70],"Hodge-Riemann":[73],"relations.":[74],"This":[75],"result":[76,97],"is":[77],"new":[78],"even":[79],"for":[80],"projectivization":[82],"an":[84],"variety.":[93],"apply":[95],"this":[96],"prove":[99],"coefficients":[102],"matroids":[104],"are":[105],"nonnegative.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}