{"id":"https://openalex.org/W7220721199","doi":"https://doi.org/10.48550/arxiv.2610.05179","title":"K-unstable Toric Varieties and Secondary Polytopes","display_name":"K-unstable Toric Varieties and Secondary Polytopes","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220721199","doi":"https://doi.org/10.48550/arxiv.2610.05179"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05179","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05179","pdf_url":"https://arxiv.org/pdf/2610.05179","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/2610.05179","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157787968","display_name":"Chi Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Chi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157710186","display_name":"Li Sheng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheng, Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5157680978","display_name":"Yi Yao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yao, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T12351","display_name":"Geometry and complex manifolds","score":0.9589999914169312,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9589999914169312,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.03880000114440918,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/k-stability","display_name":"K-stability","score":0.8479999899864197},{"id":"https://openalex.org/keywords/toric-varieties","display_name":"toric varieties","score":0.9670000076293945},{"id":"https://openalex.org/keywords/secondary-polytopes","display_name":"secondary polytopes","score":0.9700000286102295},{"id":"https://openalex.org/keywords/moment-polytopes","display_name":"moment polytopes","score":0.8759999871253967},{"id":"https://openalex.org/keywords/calabi-flow","display_name":"Calabi flow","score":0.7580000162124634},{"id":"https://openalex.org/keywords/balanced-metrics","display_name":"balanced metrics","score":0.722000002861023},{"id":"https://openalex.org/keywords/quantization","display_name":"quantization","score":0.4000000059604645}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8482999801635742},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.7890999913215637},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7786999940872192},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6122000217437744},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.49549999833106995},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4189000129699707},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.359499990940094},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2980000078678131},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05179","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05179","pdf_url":"https://arxiv.org/pdf/2610.05179","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.2610.05179","doi":"https://doi.org/10.48550/arxiv.2610.05179","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05179","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:2610.05179","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05179","pdf_url":"https://arxiv.org/pdf/2610.05179","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/W7220721199.pdf","grobid_xml":"https://content.openalex.org/works/W7220721199.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1501187898","https://openalex.org/W1946879484","https://openalex.org/W2540539825","https://openalex.org/W2799353799","https://openalex.org/W2807167974","https://openalex.org/W2994795324","https://openalex.org/W3207364540","https://openalex.org/W3212357001","https://openalex.org/W4221147761","https://openalex.org/W4397024350","https://openalex.org/W4404988936","https://openalex.org/W7106318614"],"related_works":["https://openalex.org/W4304108584","https://openalex.org/W2963052912","https://openalex.org/W7052276545","https://openalex.org/W4397024350","https://openalex.org/W2962781249","https://openalex.org/W185862059","https://openalex.org/W7212164673","https://openalex.org/W4321471380","https://openalex.org/W7221615535","https://openalex.org/W2001780303"],"abstract_inverted_index":{"For":[0],"K-unstable":[1],"toric":[2,97],"varieties,":[3],"Sz\u00e9kelyhidi's":[4],"optimal":[5],"test-function":[6],"$\u0398_{P}$":[7,44],"is":[8],"a":[9,89],"mysterious":[10],"concave":[11],"function":[12],"over":[13],"the":[14,20,27,31,49,58,63,68,72,94],"moment":[15],"polytope":[16,70],"$P$,":[17],"which":[18,54],"gives":[19],"maximal":[21,50],"destabilizer":[22],"for":[23,52,71,79],"K-stability,":[24],"and":[25,77],"encodes":[26],"limiting":[28],"behavior":[29],"of":[30,96],"divergent":[32],"Calabi":[33],"flow.":[34],"As":[35],"balanced":[36],"norms":[37],"quantize":[38],"cscK":[39],"metrics,":[40],"we":[41],"show":[42],"that":[43],"can":[45],"be":[46],"quantized":[47],"by":[48,57],"destabilizers":[51],"Chow-stability,":[53],"are":[55,83],"given":[56],"shortest":[59],"GKZ":[60],"vectors,":[61],"i.e.,":[62],"least":[64],"norm":[65],"point":[66],"on":[67],"secondary":[69],"set":[73],"$P\\cap":[74],"k^{-1}\\mathbb{Z}^{n}$.":[75],"Properties":[76],"algorithm":[78],"general":[80],"sGKZ":[81],"vectors":[82],"given.":[84],"Our":[85],"result":[86],"may":[87],"provide":[88],"new":[90],"method":[91],"to":[92],"detect":[93],"K-unstability":[95],"varieties.":[98]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
