{"id":"https://openalex.org/W7214206334","doi":"https://doi.org/10.48550/arxiv.2609.27047","title":"Degrees and directional defects of embedded algebraic vector bundles","display_name":"Degrees and directional defects of embedded algebraic vector bundles","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214206334","doi":"https://doi.org/10.48550/arxiv.2609.27047"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.27047","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27047","pdf_url":"https://arxiv.org/pdf/2609.27047","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/2609.27047","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094196411","display_name":"Leonardo Lanciano","orcid":"https://orcid.org/0009-0001-7156-2997","observed_orcids":["https://orcid.org/0009-0001-7156-2997"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lanciano, Leonardo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5094196411"],"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":0.9854000210762024,"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":0.9854000210762024,"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":0.007600000128149986,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.0035000001080334187,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/defect-theory","display_name":"defect theory","score":0.9300000071525574},{"id":"https://openalex.org/keywords/dual-defects","display_name":"dual defects","score":0.8349999785423279},{"id":"https://openalex.org/keywords/bidegree","display_name":"bidegree","score":0.8550000190734863},{"id":"https://openalex.org/keywords/van-der-waerden-s-theorem","display_name":"van der Waerden's theorem","score":0.9100000262260437},{"id":"https://openalex.org/keywords/tangent-bundle","display_name":"tangent bundle","score":0.574999988079071},{"id":"https://openalex.org/keywords/descriptor-systems","display_name":"descriptor systems","score":0.9850000143051147},{"id":"https://openalex.org/keywords/affine-varieties","display_name":"affine varieties","score":0.4309999942779541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8072999715805054},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.7908999919891357},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.5824999809265137},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49720001220703125},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4832000136375427},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4832000136375427},{"id":"https://openalex.org/C54654531","wikidata":"https://www.wikidata.org/wiki/Q6073574","display_name":"Irreducible component","level":5,"score":0.45890000462532043},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.42910000681877136},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.3961000144481659},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.38359999656677246},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.336899995803833},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.3086000084877014},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C137134375","wikidata":"https://www.wikidata.org/wiki/Q1509762","display_name":"Line bundle","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C66384103","wikidata":"https://www.wikidata.org/wiki/Q2370925","display_name":"Normal bundle","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C19485645","wikidata":"https://www.wikidata.org/wiki/Q7578745","display_name":"Splitting principle","level":3,"score":0.28610000014305115},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C144947467","wikidata":"https://www.wikidata.org/wiki/Q2397465","display_name":"Tautological line bundle","level":5,"score":0.2653999924659729},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.25369998812675476},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.2533999979496002},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2524000108242035},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.27047","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27047","pdf_url":"https://arxiv.org/pdf/2609.27047","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.2609.27047","doi":"https://doi.org/10.48550/arxiv.2609.27047","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.27047","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:2609.27047","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27047","pdf_url":"https://arxiv.org/pdf/2609.27047","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/G4391066842","display_name":null,"funder_award_id":"UBACYT 20020190100116BA","funder_id":"https://openalex.org/F4320335478","funder_display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires"},{"id":"https://openalex.org/G6522568025","display_name":null,"funder_award_id":"20020190100116BA","funder_id":"https://openalex.org/F4320335478","funder_display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires"}],"funders":[{"id":"https://openalex.org/F4320323257","display_name":"Universidad de Buenos Aires","ror":"https://ror.org/0081fs513"},{"id":"https://openalex.org/F4320335478","display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214206334.pdf","grobid_xml":"https://content.openalex.org/works/W7214206334.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7160913689"],"related_works":["https://openalex.org/W7077310641","https://openalex.org/W4409851300","https://openalex.org/W2167233579","https://openalex.org/W2964060711","https://openalex.org/W799299520","https://openalex.org/W3167938326","https://openalex.org/W1480534431","https://openalex.org/W2124624044","https://openalex.org/W7071942328","https://openalex.org/W919597372"],"abstract_inverted_index":{"We":[0,29],"develop":[1],"a":[2,17,42,61,74,100,111,162],"unified":[3],"defect":[4,52],"theory":[5,21],"for":[6,123],"embedded":[7,83,103],"algebraic":[8,104,153],"vector":[9,84,105],"bundles":[10,106],"which":[11],"places":[12],"several":[13],"classical":[14],"constructions":[15],"within":[16],"common":[18],"framework.":[19],"The":[20],"recovers":[22],"tangential,":[23],"dual,":[24],"join,":[25],"and":[26,132,159],"secant":[27],"defects.":[28],"first":[30],"prove":[31],"an":[32,82,166],"effective":[33],"numerical":[34],"criterion":[35],"characterizing":[36],"defectivity":[37],"by":[38,173],"the":[39,50,54,58,78,89,116,145],"vanishing":[40,55],"of":[41,57,63,81,92,102,107,151],"bidegree.":[43],"This":[44,97],"also":[45],"allows":[46],"us":[47],"to":[48,99,148,165],"recover":[49],"exact":[51],"from":[53,88],"pattern":[56],"bidegrees,":[59,71],"extending":[60],"theorem":[62,69],"Holme.":[64],"Using":[65],"van":[66],"der":[67],"Waerden's":[68],"on":[70],"we":[72,114,143],"obtain":[73],"formula":[75],"that":[76],"decomposes":[77],"geometric":[79],"degree":[80,157],"bundle":[85],"into":[86],"contributions":[87],"direction":[90],"varieties":[91,150],"its":[93,135],"general":[94],"linear":[95],"restrictions.":[96],"leads":[98],"characterization":[101],"minimal":[108],"degree.":[109],"As":[110],"main":[112],"application,":[113],"establish":[115],"sharp":[117],"universal":[118],"bound":[119,147],"$\\operatorname{deg}(TV)":[120],"\\leq":[121],"\\operatorname{deg}(V)^2$":[122],"every":[124],"smooth":[125],"irreducible":[126],"affine":[127],"variety":[128],"$V":[129],"\\subseteq":[130],"\\mathbb{A}^n$":[131],"$TV\\subseteq":[133],"\\mathbb{A}^{2n}$":[134],"tangent":[136],"bundle.":[137],"Finally,":[138],"under":[139],"suitable":[140],"regularity":[141],"assumptions,":[142],"apply":[144],"quadratic":[146],"prolongation":[149],"differential":[152,170],"systems,":[154],"obtaining":[155],"uniform":[156],"estimates":[158],"thereby":[160],"providing":[161],"partial":[163],"answer":[164],"open":[167],"problem":[168],"in":[169],"algebra":[171],"posed":[172],"Pogudin.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-25T00:00:00"}
