{"id":"https://openalex.org/W7220459997","doi":"https://doi.org/10.48550/arxiv.2610.02689","title":"Sharp Noether-type inequalities for $3$-folds of intermediate Kodaira dimensions","display_name":"Sharp Noether-type inequalities for $3$-folds of intermediate Kodaira dimensions","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220459997","doi":"https://doi.org/10.48550/arxiv.2610.02689"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02689","pdf_url":"https://arxiv.org/pdf/2610.02689","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/2610.02689","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157575339","display_name":"Meng Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Meng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157639724","display_name":"Yong Hu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Yong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157401537","display_name":"Chen Jiang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159985956","display_name":"Yang Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Yang","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":0.9984999895095825,"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":0.9984999895095825,"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/T12351","display_name":"Geometry and complex manifolds","score":0.0010999999940395355,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0,"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/geometric-genus","display_name":"geometric genus","score":0.9940000176429749},{"id":"https://openalex.org/keywords/canonical-systems","display_name":"canonical systems","score":0.8870000243186951},{"id":"https://openalex.org/keywords/sharp-inequalities","display_name":"sharp inequalities","score":0.6029999852180481}],"concepts":[{"id":"https://openalex.org/C2777969054","wikidata":"https://www.wikidata.org/wiki/Q6425087","display_name":"Kodaira dimension","level":2,"score":0.9789999723434448},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.7297999858856201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6385999917984009},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6129000186920166},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.5694000124931335},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5458999872207642},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3174999952316284},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.23479999601840973}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02689","pdf_url":"https://arxiv.org/pdf/2610.02689","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.2610.02689","doi":"https://doi.org/10.48550/arxiv.2610.02689","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02689","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:2610.02689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02689","pdf_url":"https://arxiv.org/pdf/2610.02689","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/G2164231362","display_name":null,"funder_award_id":"2023YFA1010600","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G2866999593","display_name":null,"funder_award_id":"#12121001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4263455182","display_name":null,"funder_award_id":"12571044","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5733081092","display_name":null,"funder_award_id":"12121001","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321851","display_name":"Fudan University","ror":"https://ror.org/013q1eq08"},{"id":"https://openalex.org/F4320335581","display_name":"Young Scientists Fund","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220459997.pdf","grobid_xml":"https://content.openalex.org/works/W7220459997.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4403796722"],"related_works":["https://openalex.org/W2895697810","https://openalex.org/W3098974571","https://openalex.org/W2085019000","https://openalex.org/W4412990916","https://openalex.org/W4416427624","https://openalex.org/W4400459745","https://openalex.org/W2476018552","https://openalex.org/W1993176485","https://openalex.org/W2254296550","https://openalex.org/W2045721877"],"abstract_inverted_index":{"For":[0],"a":[1,26,88],"smooth":[2,27],"projective":[3,28],"$3$-fold":[4,29],"$V$":[5,30,46,74,84],"of":[6,31,45,73,83,90],"intermediate":[7],"Kodaira":[8,32,43,58],"dimension,":[9],"we":[10,35,62],"establish":[11],"Noether-type":[12],"inequalities":[13,53],"relating":[14],"the":[15,20,42,57,65,70,76,80],"Iitaka":[16,77,96],"volume":[17,97],"$\\operatorname{Ivol}(V)$":[18],"and":[19,79],"geometric":[21],"genus":[22],"$p_g(V)$.":[23],"Specifically,":[24],"for":[25],"dimension":[33,44,59],"$2$,":[34],"show":[36],"that":[37,64,100],"$\\operatorname{Ivol}(V)\\geq":[38,50],"\\frac{3}{4}p_g(V)-\\frac{5}{4};$":[39],"while":[40],"if":[41,69],"is":[47,85],"$1$,":[48],"then":[49],"p_g(V)-1.$":[51],"Both":[52],"are":[54],"sharp.":[55],"In":[56],"$2$":[60],"case,":[61],"prove":[63],"equality":[66],"holds":[67],"only":[68],"bicanonical":[71],"system":[72,82],"induces":[75],"fibration":[78],"canonical":[81],"composed":[86],"with":[87],"pencil":[89],"surfaces":[91],"whose":[92],"general":[93],"member":[94],"has":[95],"$\\frac12$":[98],"provided":[99],"$p_g(V)\\geq":[101],"4$.":[102]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}
