{"id":"https://openalex.org/W7213530891","doi":"https://doi.org/10.48550/arxiv.2609.18936","title":"Relative cone of curves and contractions of a successive blowup","display_name":"Relative cone of curves and contractions of a successive blowup","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213530891","doi":"https://doi.org/10.48550/arxiv.2609.18936"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18936","pdf_url":"https://arxiv.org/pdf/2609.18936","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/2609.18936","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091957349","display_name":"Yuto Masamura","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masamura, Yuto","raw_affiliation_strings":["Graduate School of Mathematical Sciences , the University of Tokyo ,, 3-8-1 Komaba , Meguro-ku , Tokyo 153-8914 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Mathematical Sciences , the University of Tokyo ,, 3-8-1 Komaba , Meguro-ku , Tokyo 153-8914 , Japan","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091957349"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"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":0.9980000257492065,"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":0.9980000257492065,"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":0.0006000000284984708,"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":9.999999747378752e-05,"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/contractions","display_name":"contractions","score":0.8629999756813049},{"id":"https://openalex.org/keywords/normal-varieties","display_name":"normal varieties","score":0.8579999804496765},{"id":"https://openalex.org/keywords/simple-normal-crossings","display_name":"simple normal crossings","score":0.8289999961853027},{"id":"https://openalex.org/keywords/arbitrary-characteristic","display_name":"arbitrary characteristic","score":0.5220000147819519},{"id":"https://openalex.org/keywords/birational-geometry","display_name":"birational geometry","score":0.5640000104904175},{"id":"https://openalex.org/keywords/nef-divisors","display_name":"nef divisors","score":0.3109999895095825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7124000191688538},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5895000100135803},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5641000270843506},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5077000260353088},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.4754999876022339},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3862000107765198},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25220000743865967},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.23759999871253967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22699999809265137},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2167000025510788}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18936","pdf_url":"https://arxiv.org/pdf/2609.18936","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.2609.18936","doi":"https://doi.org/10.48550/arxiv.2609.18936","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18936","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:2609.18936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18936","pdf_url":"https://arxiv.org/pdf/2609.18936","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/W7213530891.pdf","grobid_xml":"https://content.openalex.org/works/W7213530891.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7125135237"],"related_works":["https://openalex.org/W120447179","https://openalex.org/W2949867080","https://openalex.org/W7095962111","https://openalex.org/W7017669244","https://openalex.org/W2913326628","https://openalex.org/W7098985744","https://openalex.org/W2082744651","https://openalex.org/W2923793991","https://openalex.org/W1572856884","https://openalex.org/W2111384627"],"abstract_inverted_index":{"Let":[0],"$X$":[1],"be":[2,13],"a":[3],"normal":[4,29],"variety":[5],"in":[6],"arbitrary":[7],"characteristic,":[8],"and":[9,31],"let":[10],"$\\tilde":[11],"X$":[12,20],"the":[14],"successive":[15],"blowup":[16],"along":[17],"subvarieties":[18],"$Z_1,\\dotsc,Z_n\\subseteq":[19],"of":[21],"codimension":[22],"at":[23],"least":[24],"two":[25],"that":[26],"have":[27],"simple":[28],"crossings":[30],"satisfy":[32],"$Z_h\\not\\supseteq":[33],"Z_i$":[34],"whenever":[35],"$h":[36]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-18T00:00:00"}