{"id":"https://openalex.org/W7204873889","doi":"https://doi.org/10.48550/arxiv.2608.28815","title":"Noncommutative Hourglasses II 1/2: Derived Category of Birational Linkage with Well-Formed Singularities","display_name":"Noncommutative Hourglasses II 1/2: Derived Category of Birational Linkage with Well-Formed Singularities","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204873889","doi":"https://doi.org/10.48550/arxiv.2608.28815"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28815","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28815","pdf_url":"https://arxiv.org/pdf/2608.28815","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/2608.28815","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148899271","display_name":"Xingbang Hao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hao, Xingbang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148899271"],"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":0.9585000276565552,"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":0.9585000276565552,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.03500000014901161,"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":0.0010000000474974513,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/toric-singularities","display_name":"toric singularities","score":0.8050000071525574},{"id":"https://openalex.org/keywords/complete-intersections","display_name":"complete intersections","score":0.6539999842643738},{"id":"https://openalex.org/keywords/derived-category-of-coherent-sheaves","display_name":"derived categories of coherent sheaves","score":0.949999988079071},{"id":"https://openalex.org/keywords/derived-stacks","display_name":"derived stacks","score":0.5410000085830688},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"noncommutative geometry","score":0.765999972820282}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8554999828338623},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7847999930381775},{"id":"https://openalex.org/C143161588","wikidata":"https://www.wikidata.org/wiki/Q906907","display_name":"Coherent sheaf","level":2,"score":0.7602999806404114},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.675599992275238},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6553999781608582},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6498000025749207},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.64410001039505},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.5946999788284302},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.5914000272750854},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C31266012","wikidata":"https://www.wikidata.org/wiki/Q6554340","display_name":"Linkage (software)","level":3,"score":0.37779998779296875},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C96881808","wikidata":"https://www.wikidata.org/wiki/Q1879333","display_name":"Birational geometry","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2809999883174896},{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28815","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28815","pdf_url":"https://arxiv.org/pdf/2608.28815","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.2608.28815","doi":"https://doi.org/10.48550/arxiv.2608.28815","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28815","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:2608.28815","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28815","pdf_url":"https://arxiv.org/pdf/2608.28815","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204873889.pdf","grobid_xml":"https://content.openalex.org/works/W7204873889.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1679005091","https://openalex.org/W2144392866","https://openalex.org/W4394668478","https://openalex.org/W4404089390","https://openalex.org/W4404987235","https://openalex.org/W4406975448","https://openalex.org/W7075993999"],"related_works":["https://openalex.org/W7096268533","https://openalex.org/W7096489436","https://openalex.org/W4385559712","https://openalex.org/W2082666973","https://openalex.org/W2258494900","https://openalex.org/W4301458152","https://openalex.org/W6940414487","https://openalex.org/W2115057135","https://openalex.org/W4406975448","https://openalex.org/W4253339618"],"abstract_inverted_index":{"We":[0],"consider":[1],"varieties":[2],"whose":[3],"singularities":[4],"are":[5],"complete":[6],"intersections":[7],"within":[8],"toric":[9],"singularities,":[10],"which":[11],"we":[12,23,42],"call":[13],"well-formed":[14],"varieties.":[15],"Using":[16],"the":[17,30,45],"construction":[18],"of":[19,33],"equivariant":[20],"standard":[21],"resolutions,":[22],"can":[24],"extend":[25],"several":[26],"classical":[27],"formulas":[28],"in":[29],"derived":[31],"category":[32],"bounded":[34],"coherent":[35],"sheaves":[36],"to":[37],"this":[38],"singular":[39],"setting.":[40],"Finally,":[41],"also":[43],"discuss":[44],"Bondal--Orlov":[46],"localization":[47],"for":[48],"certain":[49],"morphisms":[50],"between":[51],"terminal":[52],"complex":[53],"threefolds":[54],"and":[55],"their":[56],"stacks.":[57]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
