{"id":"https://openalex.org/W7222954005","doi":"https://doi.org/10.48550/arxiv.2610.23485","title":"Lefschetz Pencils on surfaces and an application to Seshadri constants","display_name":"Lefschetz Pencils on surfaces and an application to Seshadri constants","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222954005","doi":"https://doi.org/10.48550/arxiv.2610.23485"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.23485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23485","pdf_url":"https://arxiv.org/pdf/2610.23485","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/2610.23485","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159070355","display_name":"Krishna Hanumanthu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Hanumanthu, Krishna","raw_affiliation_strings":["Chennai Mathematical Institute , H1 SIPCOT IT Park , Siruseri , Kelambakkam 603103 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute , H1 SIPCOT IT Park , Siruseri , Kelambakkam 603103 , India","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042846961","display_name":"A. J. Parameswaran","orcid":"https://orcid.org/0000-0003-2527-1141","observed_orcids":["https://orcid.org/0000-0003-2527-1141"]},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]},{"id":"https://openalex.org/I2800520468","display_name":"Kerala School of Mathematics","ror":"https://ror.org/02wjedj15","country_code":"IN","type":"education","lineage":["https://openalex.org/I2800520468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Parameswaran, A. J.","raw_affiliation_strings":["Chennai Mathematical Institute , H1 SIPCOT IT Park , Siruseri , Kelambakkam 603103 , India","Kerala School of Mathematics , Kunnamangalam PO , Kozhikode , Kerala , 673571 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute , H1 SIPCOT IT Park , Siruseri , Kelambakkam 603103 , India","institution_ids":["https://openalex.org/I19149307"]},{"raw_affiliation_string":"Kerala School of Mathematics , Kunnamangalam PO , Kozhikode , Kerala , 673571 , India","institution_ids":["https://openalex.org/I2800520468"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":1.0,"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":1.0,"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":0.0,"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/lefschetz-pencils","display_name":"Lefschetz pencils","score":1.0},{"id":"https://openalex.org/keywords/seshadri-constants","display_name":"Seshadri constants","score":0.972000002861023},{"id":"https://openalex.org/keywords/complex-projective-surfaces","display_name":"complex projective surfaces","score":0.8119999766349792},{"id":"https://openalex.org/keywords/very-ample-line-bundles","display_name":"very ample line bundles","score":0.902999997138977},{"id":"https://openalex.org/keywords/vanishing-cycles","display_name":"vanishing cycles","score":0.8769999742507935},{"id":"https://openalex.org/keywords/irregularity","display_name":"irregularity","score":0.597000002861023},{"id":"https://openalex.org/keywords/blow-up","display_name":"blow-up","score":0.6740000247955322},{"id":"https://openalex.org/keywords/linear-systems-of-curves","display_name":"linear systems of curves","score":0.5630000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8687000274658203},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6603000164031982},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6528000235557556},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.5989999771118164},{"id":"https://openalex.org/C40926966","wikidata":"https://www.wikidata.org/wiki/Q4748472","display_name":"Ample line bundle","level":2,"score":0.5608999729156494},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3165999948978424},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C123635137","wikidata":"https://www.wikidata.org/wiki/Q840376","display_name":"Ruled surface","level":3,"score":0.2759999930858612},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C106142965","wikidata":"https://www.wikidata.org/wiki/Q1969721","display_name":"K3 surface","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.2680000066757202},{"id":"https://openalex.org/C137134375","wikidata":"https://www.wikidata.org/wiki/Q1509762","display_name":"Line bundle","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C90685605","wikidata":"https://www.wikidata.org/wiki/Q764115","display_name":"Projective line","level":4,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.23485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23485","pdf_url":"https://arxiv.org/pdf/2610.23485","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.2610.23485","doi":"https://doi.org/10.48550/arxiv.2610.23485","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.23485","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:2610.23485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23485","pdf_url":"https://arxiv.org/pdf/2610.23485","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":[{"id":"https://openalex.org/F4320306227","display_name":"Arthritis National Research Foundation","ror":"https://ror.org/03abbex33"},{"id":"https://openalex.org/F4320322753","display_name":"Infosys Foundation","ror":"https://ror.org/03bs18y54"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222954005.pdf","grobid_xml":"https://content.openalex.org/works/W7222954005.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2807583486","https://openalex.org/W7221983977","https://openalex.org/W1992757100","https://openalex.org/W2950960952","https://openalex.org/W7128614888","https://openalex.org/W2510054580","https://openalex.org/W7166587042","https://openalex.org/W2607419603","https://openalex.org/W3005965176","https://openalex.org/W4404431311"],"abstract_inverted_index":{"Let":[0],"$X$":[1],"be":[2,11],"a":[3,12,25,42,61,89,105,123],"nonsingular":[4],"complex":[5],"projective":[6],"surface":[7],"and":[8,37,55,78,122],"let":[9],"$L$":[10],"very":[13],"ample":[14,116],"line":[15,117],"bundle":[16,118],"on":[17,120],"$X$.":[18,70],"We":[19,40],"study":[20],"the":[21,29,58,67,79],"question:":[22],"when":[23,136],"does":[24],"general":[26,62],"pencil":[27],"in":[28,50],"linear":[30],"system":[31],"$|L|$":[32,65],"consist":[33],"of":[34,60,64,69,81],"only":[35,56],"irreducible":[36],"reduced":[38],"curves?":[39],"give":[41],"precise":[43],"condition":[44],"which":[45],"guarantees":[46],"an":[47,85,115],"affirmative":[48],"answer:":[49],"fact,":[51],"this":[52,135],"holds":[53],"if":[54,57],"genus":[59],"member":[63],"exceeds":[66],"irregularity":[68],"The":[71],"proof":[72],"is":[73],"topological,":[74],"using":[75],"vanishing":[76],"cycles":[77],"theory":[80],"Lefschetz":[82],"pencils.":[83],"As":[84],"application,":[86],"combined":[87],"with":[88],"construction":[90],"due":[91],"to":[92],"Miranda,":[93],"we":[94],"prove":[95],"that":[96,129],"for":[97],"any":[98],"positive":[99],"rational":[100],"number":[101],"$\u03b4$":[102],"there":[103],"exist":[104],"blow":[106],"up":[107],"$Y":[108],"\\to":[109],"X$":[110],"at":[111],"finitely":[112],"many":[113],"points,":[114],"$M$":[119],"$Y$":[121],"point":[124],"$x":[125],"\\in":[126],"Y$":[127],"such":[128],"$\\varepsilon(Y,M,x)":[130],"=":[131,138],"\u03b4$;":[132],"Miranda":[133],"proved":[134],"$X":[137],"\\mathbb{P}^2$.":[139]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-20T00:00:00"}
