{"id":"https://openalex.org/W7220902397","doi":"https://doi.org/10.48550/arxiv.2610.10230","title":"Minkowski decompositions and universal equivariant deformations of toric pairs","display_name":"Minkowski decompositions and universal equivariant deformations of toric pairs","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220902397","doi":"https://doi.org/10.48550/arxiv.2610.10230"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10230","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10230","pdf_url":"https://arxiv.org/pdf/2610.10230","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/2610.10230","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035423168","display_name":"Matej Filip","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Filip, Matej","raw_affiliation_strings":["UNIVERSITY OF LJUBLJANA , INSTITUTE OF MATHEMATICS , PHYSICS AND MECHANICS , TRZASKA CESTA 25 , LJUBLJANA , SLOVENIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UNIVERSITY OF LJUBLJANA , INSTITUTE OF MATHEMATICS , PHYSICS AND MECHANICS , TRZASKA CESTA 25 , LJUBLJANA , SLOVENIA","institution_ids":["https://openalex.org/I153976015","https://openalex.org/I4210106342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035423168"],"corresponding_institution_ids":["https://openalex.org/I153976015","https://openalex.org/I4210106342"],"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":0.9634000062942505,"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":0.9634000062942505,"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":0.02459999918937683,"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"}},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.00279999990016222,"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/equivariant-vector-bundles","display_name":"equivariant vector bundles","score":0.5799999833106995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8246999979019165},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7962999939918518},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.6639999747276306},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6270999908447266},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5687999725341797},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.5414999723434448},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.45730000734329224},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.3970000147819519},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3808000087738037},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.37959998846054077},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.27649998664855957},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.2669999897480011},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10230","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10230","pdf_url":"https://arxiv.org/pdf/2610.10230","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.2610.10230","doi":"https://doi.org/10.48550/arxiv.2610.10230","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10230","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:2610.10230","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10230","pdf_url":"https://arxiv.org/pdf/2610.10230","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/W7220902397.pdf","grobid_xml":"https://content.openalex.org/works/W7220902397.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3036450870","https://openalex.org/W1629558705","https://openalex.org/W4414277622","https://openalex.org/W2075089865","https://openalex.org/W1551584734","https://openalex.org/W1974146564","https://openalex.org/W3100507185","https://openalex.org/W2284371390","https://openalex.org/W1613665986","https://openalex.org/W7047382336"],"abstract_inverted_index":{"Let":[0],"$X_\u03c3$":[1],"be":[2,21],"the":[3,51,55,69,86],"affine":[4,99],"normal":[5,100],"toric":[6,101],"variety":[7],"associated":[8],"with":[9,25],"a":[10,22,80],"full-dimensional":[11],"strongly":[12],"convex":[13],"rational":[14],"polyhedral":[15],"cone":[16],"$\u03c3$,":[17],"and":[18,67,94,103],"let":[19],"$m$":[20],"primitive":[23,105],"degree":[24],"slice":[26],"$P_m=\u03c3\\cap[m=1]$.":[27],"We":[28,48],"construct":[29],"an":[30],"explicit":[31],"flat":[32],"algebraic":[33],"family":[34,71,84],"whose":[35],"completion":[36],"is":[37],"universal":[38,82],"for":[39,85],"equivariant":[40,83],"deformations":[41],"in":[42],"all":[43],"degrees":[44],"$-jm$,":[45],"$j\\ge1$,":[46],"simultaneously.":[47],"prove":[49],"that":[50],"irreducible":[52],"components":[53],"of":[54,65],"reduced":[56],"base":[57],"correspond":[58],"bijectively":[59],"to":[60,97],"maximal":[61],"lattice-friendly":[62],"Minkowski":[63],"decompositions":[64],"$P_m$,":[66],"describe":[68],"induced":[70],"on":[72],"each":[73],"component.":[74],"When":[75],"$m\\in\u03c3^\\vee$,":[76],"we":[77],"also":[78],"obtain":[79],"formally":[81],"pair":[87],"$(X_\u03c3,V(\u03c7^m))$.":[88],"These":[89],"results":[90],"extend":[91],"earlier":[92],"miniversality":[93],"component":[95],"theorems":[96],"arbitrary":[98,104],"varieties":[102],"degrees.":[106]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-09T00:00:00"}
