{"id":"https://openalex.org/W2109495391","doi":"https://doi.org/10.48550/arxiv.1310.1865","title":"Notes on Hilbert's 16th: experiencing Viro's theory","display_name":"Notes on Hilbert's 16th: experiencing Viro's theory","publication_year":2013,"publication_date":"2013-10-07","ids":{"openalex":"https://openalex.org/W2109495391","doi":"https://doi.org/10.48550/arxiv.1310.1865","mag":"2109495391"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1310.1865","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.1865","pdf_url":"https://arxiv.org/pdf/1310.1865","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/1310.1865","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074929511","display_name":"Alexandre Gabard","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gabard, Alexandre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5074929511"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9951000213623047,"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":0.9951000213623047,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0010999999940395355,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0008999999845400453,"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/hilbert-s-16th-problem","display_name":"Hilbert's 16th problem","score":0.9779999852180481},{"id":"https://openalex.org/keywords/bezout-theorem","display_name":"Bezout theorem","score":0.6480000019073486},{"id":"https://openalex.org/keywords/real-algebraic-curves","display_name":"real algebraic curves","score":0.6800000071525574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4877787232398987},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4231807589530945}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1310.1865","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.1865","pdf_url":"https://arxiv.org/pdf/1310.1865","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":"pmh:oai:CiteSeerX.psu:10.1.1.739.9428","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.739.9428","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1310.1865.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1310.1865","doi":"https://doi.org/10.48550/arxiv.1310.1865","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1310.1865","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1310.1865","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.1865","pdf_url":"https://arxiv.org/pdf/1310.1865","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"This":[0,70,118],"text":[1],"is":[2,54,71,148,217],"intended":[3],"to":[4,17,31,34,46,57,128,151,169,179,226,240],"become":[5],"in":[6,67,161,174,191],"the":[7,61,110,125,133,144,146,175,181,192,215,229],"long":[8,14,203],"run":[9],"Chapter":[10],"3":[11],"of":[12,76,98,103,138,165,184,188],"our":[13,32,52],"saga":[15],"dedicated":[16],"Riemann,":[18],"Ahlfors":[19],"and":[20,109,132,172,206],"Rohlin.":[21],"Yet,":[22],"as":[23,27,38,40,129,178],"its":[24],"contents":[25],"evolved":[26],"mostly":[28],"independent":[29],"(due":[30],"inaptitude":[33],"interconnect":[35],"both":[36],"trends":[37],"strongly":[39],"we":[41],"wished),":[42],"it":[43,48],"seemed":[44],"preferable":[45],"publish":[47],"separately.":[49],"More":[50],"factually,":[51],"account":[53],"an":[55],"attempt":[56],"get":[58],"familiarized":[59],"with":[60,163,219],"current":[62],"consensus":[63],"about":[64],"Hilbert's":[65],"16th":[66],"degree":[68],"8.":[69],"a":[72,96,152,189],"nearly":[73],"finished":[74],"piece":[75],"mathematics,":[77],"thanks":[78],"heroic":[79],"breakthroughs":[80],"by":[81],"Viro,":[82,140],"Fiedler,":[83,139],"Korchagin,":[84],"Shustin,":[85,141],"Chevallier,":[86],"Orevkov,":[87],"yet":[88,231],"still":[89,220],"leaving":[90],"undecided":[91],"six":[92,221],"tantalizing":[93],"bosons":[94],"among":[95],"menagerie":[97],"104":[99],"logically":[100],"possible":[101],"distributions":[102],"ovals":[104],"(respecting":[105],"B\u00e9zout,":[106],"Gudkov":[107],"periodicity,":[108],"Fiedler-Viro":[111],"imparity":[112],"law":[113],"sieving":[114],"away":[115],"4+36":[116],"schemes).":[117],"quest":[119],"inevitably":[120],"involves":[121],"glimpsing":[122],"deep":[123],"into":[124],"nebula":[126],"referrable":[127],"Viro's":[130],"patchworking,":[131],"likewise":[134],"spectacular":[135],"obstructional":[136],"laws":[137],"Orevkov.":[142],"In":[143],"overall,":[145],"game":[147],"much":[149],"comparable":[150],"pigeons":[153],"hunting":[154],"video-game,":[155],"where":[156],"144":[157],"birds":[158,199],"are":[159],"liberated":[160],"nature,":[162],"some":[164],"them":[166,242],"strong":[167],"enough":[168,239],"fly":[170],"higher":[171,173],"blue":[176],"sky":[177],"rejoin":[180],"stratospheric":[182],"paradise":[183],"eternal":[185],"life":[186],"(construction":[187],"scheme":[190],"algebro-geometric":[193],"category).":[194],"Some":[195],"other,":[196],"less":[197],"fortunate,":[198],"were":[200],"killed":[201],"(a":[202],"time":[204],"ago)":[205],"crashed":[207],"down":[208],"miserably":[209],"over":[210],"terrestrial":[211],"crust":[212],"(prohibition).":[213],"Alas,":[214],"hunt":[216],"unfinished":[218],"birds,":[222],"apparently":[223],"too":[224,232],"feeble":[225],"rally":[227],"safely":[228],"paradise,":[230],"acrobatic":[233],"for":[234],"any":[235],"homosapiens":[236],"being":[237],"skillful":[238],"shoot":[241],"down.":[243]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}