{"id":"https://openalex.org/W7214368283","doi":"https://doi.org/10.48550/arxiv.2609.29654","title":"On the Analyticity of Amoeba Contours","display_name":"On the Analyticity of Amoeba Contours","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7214368283","doi":"https://doi.org/10.48550/arxiv.2609.29654"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29654","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29654","pdf_url":"https://arxiv.org/pdf/2609.29654","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/2609.29654","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013137097","display_name":"Mounir Nisse","orcid":"https://orcid.org/0000-0003-0455-0600","observed_orcids":["https://orcid.org/0000-0003-0455-0600"]},"institutions":[{"id":"https://openalex.org/I4210134189","display_name":"Xiamen University Malaysia","ror":"https://ror.org/0331wa828","country_code":"MY","type":"education","lineage":["https://openalex.org/I191208505","https://openalex.org/I4210134189"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Nisse, Mounir","raw_affiliation_strings":["Department of Mathematics , Xiamen University Malaysia , Jalan Sunsuria , Bandar Sunsuria , 43900 , Sepang , Selangor , Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Xiamen University Malaysia , Jalan Sunsuria , Bandar Sunsuria , 43900 , Sepang , Selangor , Malaysia","institution_ids":["https://openalex.org/I4210134189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013137097"],"corresponding_institution_ids":["https://openalex.org/I4210134189"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.9839000105857849,"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":0.9839000105857849,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.008299999870359898,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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/logarithmic-map","display_name":"logarithmic map","score":0.7839999794960022},{"id":"https://openalex.org/keywords/critical-values","display_name":"critical values","score":0.5139999985694885},{"id":"https://openalex.org/keywords/semialgebraic-sets","display_name":"semialgebraic sets","score":0.8040000200271606},{"id":"https://openalex.org/keywords/real-analytic-hypersurfaces","display_name":"real analytic hypersurfaces","score":0.8550000190734863},{"id":"https://openalex.org/keywords/algebraic-hypersurfaces","display_name":"algebraic hypersurfaces","score":0.7710000276565552},{"id":"https://openalex.org/keywords/critical-locus","display_name":"critical locus","score":0.5609999895095825},{"id":"https://openalex.org/keywords/tropical-geometry","display_name":"tropical geometry","score":0.41999998688697815}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8224999904632568},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.5745000243186951},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.5720999836921692},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5604000091552734},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5113999843597412},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.484499990940094},{"id":"https://openalex.org/C2776172558","wikidata":"https://www.wikidata.org/wiki/Q46729","display_name":"Amoeba (genus)","level":2,"score":0.4738999903202057},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.444599986076355},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4147000014781952},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4004000127315521},{"id":"https://openalex.org/C86069527","wikidata":"https://www.wikidata.org/wiki/Q6653802","display_name":"Contour line","level":2,"score":0.398499995470047},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3747999966144562},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C2776441312","wikidata":"https://www.wikidata.org/wiki/Q575710","display_name":"Gauss map","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.2897000014781952},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.27649998664855957},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26989999413490295},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29654","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29654","pdf_url":"https://arxiv.org/pdf/2609.29654","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.2609.29654","doi":"https://doi.org/10.48550/arxiv.2609.29654","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29654","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:2609.29654","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29654","pdf_url":"https://arxiv.org/pdf/2609.29654","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/W7214368283.pdf","grobid_xml":"https://content.openalex.org/works/W7214368283.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2056254807"],"related_works":["https://openalex.org/W7162410401","https://openalex.org/W7172526422","https://openalex.org/W7221754868","https://openalex.org/W7169796415","https://openalex.org/W2041600451","https://openalex.org/W1546014951","https://openalex.org/W4234922555","https://openalex.org/W1982024589","https://openalex.org/W7095398763","https://openalex.org/W2516751240"],"abstract_inverted_index":{"The":[0],"contour":[1,45,67,125,162],"of":[2,9,30,43,46,127,137,160,166,174],"an":[3],"amoeba":[4,31],"records":[5],"the":[6,10,27,35,39,44,66,73,83,148,157,161,164,172],"critical":[7,91,105,144,168],"values":[8],"logarithmic":[11,74,84,149],"map":[12,76,85,150],"and":[13,22,82,170,177],"forms":[14],"a":[15,56,61,69,133,142],"fundamental":[16],"interface":[17],"between":[18],"complex":[19],"algebraic":[20,48],"geometry":[21,159],"real-analytic":[23,71,111,143],"geometry.":[24],"Building":[25],"on":[26,146],"known":[28],"semianalyticity":[29],"contours,":[32],"we":[33,59,114],"prove":[34],"stronger":[36],"statement":[37],"that":[38,65,96],"componentwise":[40],"exponential":[41],"image":[42],"any":[47],"hypersurface":[49],"in":[50],"$(\\mathbb":[51],"C^*)^n$":[52],"is":[53,68,77,99,130],"semialgebraic.":[54],"For":[55],"smooth":[57],"hypersurface,":[58],"establish":[60],"natural":[62],"criterion":[63],"guaranteeing":[64],"closed":[70],"hypersurface:":[72],"Gauss":[75],"transverse":[78],"to":[79],"$\\mathbb":[80],"RP^{n-1}$":[81],"has":[86,151],"maximal":[87,152],"rank":[88],"along":[89],"its":[90,138,167],"locus.":[92],"We":[93],"then":[94],"show":[95],"neither":[97],"hypothesis":[98],"necessary,":[100],"since":[101],"singular":[102],"or":[103],"ramified":[104],"parametrizations":[106],"may":[107],"still":[108],"have":[109],"complete":[110],"images.":[112],"Finally,":[113],"derive":[115],"intrinsic":[116],"restrictions":[117],"imposed":[118],"by":[119,141],"analyticity.":[120,184],"In":[121],"particular,":[122],"every":[123],"irreducible":[124],"component":[126],"dimension":[128],"$n-1$":[129],"generated,":[131],"over":[132],"dense":[134],"open":[135],"subset":[136],"regular":[139],"locus,":[140],"stratum":[145],"which":[147],"rank.":[153],"These":[154],"results":[155],"distinguish":[156],"analytic":[158],"from":[163],"singularities":[165],"parametrization":[169],"answer":[171],"question":[173],"Lang,":[175],"Shapiro,":[176],"Shustin":[178],"concerning":[179],"effective":[180],"sufficient":[181],"conditions":[182],"for":[183]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}