{"id":"https://openalex.org/W7215124390","doi":"https://doi.org/10.48550/arxiv.2609.39309","title":"Normal Bundle Splitting Strata of Rational Curves in Toric Varieties","display_name":"Normal Bundle Splitting Strata of Rational Curves in Toric Varieties","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7215124390","doi":"https://doi.org/10.48550/arxiv.2609.39309"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.39309","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39309","pdf_url":"https://arxiv.org/pdf/2609.39309","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/2609.39309","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140797579","display_name":"Hikari Iwasaki","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Iwasaki, Hikari","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5140797579"],"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/rational-curves","display_name":"rational curves","score":0.7129999995231628},{"id":"https://openalex.org/keywords/toric-varieties","display_name":"toric varieties","score":0.9819999933242798},{"id":"https://openalex.org/keywords/stratification","display_name":"stratification","score":0.574999988079071},{"id":"https://openalex.org/keywords/universal-curve","display_name":"universal curve","score":0.49399998784065247},{"id":"https://openalex.org/keywords/vector-bundles","display_name":"vector bundles","score":0.4399999976158142}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9122999906539917},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.6779999732971191},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6610999703407288},{"id":"https://openalex.org/C137134375","wikidata":"https://www.wikidata.org/wiki/Q1509762","display_name":"Line bundle","level":2,"score":0.6032999753952026},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.5356000065803528},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.5202999711036682},{"id":"https://openalex.org/C62139920","wikidata":"https://www.wikidata.org/wiki/Q3554818","display_name":"Projective variety","level":2,"score":0.5019000172615051},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.47769999504089355},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C66384103","wikidata":"https://www.wikidata.org/wiki/Q2370925","display_name":"Normal bundle","level":3,"score":0.41850000619888306},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.390500009059906},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3840999901294708},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.36809998750686646},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.36739999055862427},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C44594293","wikidata":"https://www.wikidata.org/wiki/Q1062978","display_name":"Characteristic class","level":3,"score":0.3156999945640564},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C144947467","wikidata":"https://www.wikidata.org/wiki/Q2397465","display_name":"Tautological line bundle","level":5,"score":0.30799999833106995},{"id":"https://openalex.org/C90685605","wikidata":"https://www.wikidata.org/wiki/Q764115","display_name":"Projective line","level":4,"score":0.302700012922287},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C151527765","wikidata":"https://www.wikidata.org/wiki/Q1069818","display_name":"Chern class","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C37500760","wikidata":"https://www.wikidata.org/wiki/Q7858555","display_name":"Twisted cubic","level":5,"score":0.27250000834465027},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.39309","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39309","pdf_url":"https://arxiv.org/pdf/2609.39309","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.2609.39309","doi":"https://doi.org/10.48550/arxiv.2609.39309","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.39309","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:2609.39309","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39309","pdf_url":"https://arxiv.org/pdf/2609.39309","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/W7215124390.pdf","grobid_xml":"https://content.openalex.org/works/W7215124390.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W78597518","https://openalex.org/W164395393","https://openalex.org/W1617797638","https://openalex.org/W1964434874","https://openalex.org/W1978619025","https://openalex.org/W1992727524","https://openalex.org/W2073267995","https://openalex.org/W2086001387","https://openalex.org/W2093283971","https://openalex.org/W2481726583","https://openalex.org/W2526605305","https://openalex.org/W2617434291","https://openalex.org/W3009448795","https://openalex.org/W3087991662","https://openalex.org/W3119306777","https://openalex.org/W4205502224","https://openalex.org/W4245842230","https://openalex.org/W4387545074","https://openalex.org/W4394838693","https://openalex.org/W7167243559"],"related_works":["https://openalex.org/W4405904212","https://openalex.org/W2253867277","https://openalex.org/W2073267995","https://openalex.org/W6889147032","https://openalex.org/W4399807229","https://openalex.org/W4379616827","https://openalex.org/W2951052196","https://openalex.org/W7097347491","https://openalex.org/W2593785924","https://openalex.org/W3150205562"],"abstract_inverted_index":{"We":[0,104,131],"study":[1],"stratification":[2],"by":[3,45],"normal-bundle":[4],"splitting":[5,83],"type":[6,84],"in":[7,16],"families":[8],"of":[9,13,40,48,64,88,100,110,128,141],"unramified":[10],"rational":[11],"curves":[12],"fixed":[14],"class":[15],"a":[17],"smooth":[18],"projective":[19,111],"toric":[20],"variety":[21],"over":[22,55],"an":[23,36],"algebraically":[24],"closed":[25],"field":[26],"{of":[27],"arbitrary":[28],"characteristic}.":[29],"Using":[30],"the":[31,41,52,56,68,89,101,119,137,142],"Cox":[32],"construction,":[33],"we":[34,61,72,79,93],"construct":[35,62],"explicit":[37,134],"two-term":[38],"resolution":[39],"relative":[42,74],"normal":[43,102],"bundle":[44],"direct":[46],"sums":[47],"line":[49],"bundles":[50,66],"on":[51,67],"universal":[53],"curve":[54],"fixed-source":[57],"parameter":[58,69],"space.":[59],"Then":[60],"morphisms":[63],"vector":[65],"space,":[70],"which":[71,78],"call":[73],"cohomology":[75],"morphisms,":[76],"from":[77],"can":[80],"investigate":[81],"generic":[82],"and":[85,116],"jumping":[86],"loci":[87],"family.":[90],"In":[91],"particular,":[92],"obtain":[94,133],"sufficient":[95],"numerical":[96,120],"criteria":[97,121],"for":[98,122,136],"unbalancedness":[99,123],"bundle.":[103],"apply":[105],"this":[106],"method":[107],"to":[108,126],"blowups":[109],"space":[112],"along":[113],"linear":[114],"subspaces,":[115],"show":[117],"that":[118],"are":[124],"equivalent":[125],"those":[127],"Cela--Lian":[129],"\\cite{CelaLian2026}.":[130],"also":[132],"formulas":[135],"expected":[138],"Chow":[139],"classes":[140],"jump":[143],"loci.":[144]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-02T00:00:00"}
