{"id":"https://openalex.org/W7213416855","doi":"https://doi.org/10.48550/arxiv.2609.17469","title":"Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves","display_name":"Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213416855","doi":"https://doi.org/10.48550/arxiv.2609.17469"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17469","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17469","pdf_url":"https://arxiv.org/pdf/2609.17469","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.17469","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151913995","display_name":"Yi Lu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lu, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151913995"],"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":0.9887999892234802,"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":0.9887999892234802,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0044999998062849045,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.0024999999441206455,"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/newton-okounkov-bodies","display_name":"Newton-Okounkov bodies","score":0.9679999947547913},{"id":"https://openalex.org/keywords/products-of-curves","display_name":"products of curves","score":0.9350000023841858},{"id":"https://openalex.org/keywords/smooth-projective-curves","display_name":"smooth projective curves","score":0.7630000114440918},{"id":"https://openalex.org/keywords/decreasing-rearrangement","display_name":"decreasing rearrangement","score":0.8109999895095825},{"id":"https://openalex.org/keywords/flags","display_name":"flags","score":0.5479999780654907}],"concepts":[{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.8361999988555908},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8284000158309937},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.7888000011444092},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6258000135421753},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4970000088214874},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.461899995803833},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.45159998536109924},{"id":"https://openalex.org/C79013991","wikidata":"https://www.wikidata.org/wiki/Q1097021","display_name":"Minkowski's theorem","level":3,"score":0.4422999918460846},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.41499999165534973},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3774999976158142},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.311599999666214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30809998512268066},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.2944999933242798},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C153011950","wikidata":"https://www.wikidata.org/wiki/Q10310534","display_name":"Infinitesimal transformation","level":3,"score":0.2587999999523163}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17469","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17469","pdf_url":"https://arxiv.org/pdf/2609.17469","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.2609.17469","doi":"https://doi.org/10.48550/arxiv.2609.17469","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17469","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.17469","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17469","pdf_url":"https://arxiv.org/pdf/2609.17469","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/W7213416855.pdf","grobid_xml":"https://content.openalex.org/works/W7213416855.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4416113484","https://openalex.org/W1965041703","https://openalex.org/W1499662896","https://openalex.org/W2468152844","https://openalex.org/W1613665986","https://openalex.org/W4212819050","https://openalex.org/W7096559643","https://openalex.org/W2269580906","https://openalex.org/W2899131131","https://openalex.org/W6966805748"],"abstract_inverted_index":{"Explicit":[0],"computations":[1],"of":[2,31,41,98,104],"generic":[3],"infinitesimal":[4],"Newton--Okounkov":[5],"bodies":[6,88],"are":[7,59],"difficult":[8],"even":[9],"for":[10,24,37,73],"varieties":[11],"with":[12],"simple":[13],"product":[14],"structure.":[15],"We":[16],"give":[17,69],"an":[18],"explicit":[19,52],"formula":[20],"in":[21,75],"arbitrary":[22],"dimension":[23],"positive-degree":[25],"external":[26],"tensor":[27],"products":[28,30],"on":[29,92],"smooth":[32],"projective":[33],"curves.":[34],"Writing":[35],"$d^\\downarrow=(d_1^\\downarrow,\\ldots,d_n^\\downarrow)$":[36],"the":[38,42,48,51,57,60,76],"decreasing":[39,102],"rearrangement":[40],"degree":[43,106],"vector":[44],"and":[45],"setting":[46],"$d_{n+1}^\\downarrow=0$,":[47],"body":[49],"admits":[50],"Minkowski":[53,77],"decomposition":[54],"$\\sum_{j=1}^n(d_j^\\downarrow-d_{j+1}^\\downarrow)S_j^{(n)}$,":[55],"where":[56],"$S_j^{(n)}$":[58],"embedded":[61],"simplices":[62],"defined":[63],"below.":[64],"Using":[65],"this":[66],"description,":[67],"we":[68],"a":[70,93],"sharp":[71],"criterion":[72],"equality":[74],"inclusion.":[78],"A":[79],"simultaneous":[80],"relabeling":[81],"argument":[82],"also":[83],"allows":[84],"finitely":[85],"many":[86],"such":[87],"to":[89],"be":[90],"realized":[91],"common":[94],"very":[95],"general":[96],"locus":[97],"flags":[99],"after":[100],"independent":[101],"rearrangements":[103],"their":[105],"vectors.":[107]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-17T00:00:00"}