{"doi":"10.1007/s11856-012-0129-6","title":"Recovering plane curves of low degree from their inflection lines and inflection points","abstract":"<jats:title>Abstract</jats:title>\n          <jats:p>In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree <jats:italic>d</jats:italic> ≥ 3 from its inflection lines? We answer the posed question positively for a general smooth plane quartic curve, making the additional assumption that also one inflection point is given, and for any smooth plane cubic curve.</jats:p>","journal":"Israel Journal of Mathematics","year":2013,"id":689892,"datarank":0.20794415416798362,"base_score":1.3862943611198906,"endowment":1.3862943611198906,"self_citation_contribution":0.20794415416798362,"citation_network_contribution":0.0,"self_endowment_contribution":0.20794415416798362,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":3,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1802313,"name":"Damiano Testa","orcid":null,"position":1,"is_corresponding":false},{"id":1802312,"name":"Marco Pacini","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Recovering plane curves of low degree from their inflection lines and inflection points","abstract":"<jats:title>Abstract</jats:title>\n          <jats:p>In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree <jats:italic>d</jats:italic> ≥ 3 from its inflection lines? We answer the posed question positively for a general smooth plane quartic curve, making the additional assumption that also one inflection point is given, and for any smooth plane cubic curve.</jats:p>","is_dataset_classified":null,"base_score":1.3862943611198906,"endowment":1.3862943611198906,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21097893","pmcid":null,"openalex_id":"https://openalex.org/W2099571829","authors":[],"funders":[{"funder_name":"UK Research and Innovation","grant_id":"EP/F060661/1","title":"Algebraic and Analytic Methods in Number Theory."}],"total_grants":1,"fwci":0.3698,"citation_percentile":0.5877017,"influential_citations":0,"citation_trend":[{"year":2014,"count":1},{"year":2019,"count":1},{"year":2020,"count":1}],"oa_status":"hybrid","license":"cc-by","oa_locations":[{"url":"https://link.springer.com/content/pdf/10.1007/s11856-012-0129-6.pdf","host_type":"journal"},{"url":"https://link.springer.com/content/pdf/10.1007/s11856-012-0129-6.pdf","host_type":"publisher"},{"url":"https://link.springer.com/article/10.1007/s11856-012-0129-6/fulltext.html","host_type":"publisher"},{"url":"http://link.springer.com/content/pdf/10.1007/s11856-012-0129-6","host_type":"publisher"},{"url":"https://doi.org/10.1007/s11856-012-0129-6","host_type":"journal"},{"url":"https://link.springer.com/content/pdf/10.1007%2Fs11856-012-0129-6.pdf","host_type":""},{"url":"https://dx.doi.org/10.48550/arxiv.1110.3082","host_type":""},{"url":"http://arxiv.org/abs/1110.3082","host_type":""},{"url":"https://zbmath.org/6221755","host_type":""},{"url":"http://dx.doi.org/10.1007/s11856-012-0129-6","host_type":""},{"url":"https://dx.doi.org/10.1007/s11856-012-0129-6","host_type":""}],"fields_of_study":["Algebraic Geometry and Number Theory","Advanced Numerical Analysis Techniques","Polynomial and algebraic computation","0103 physical sciences","0101 mathematics","01 natural sciences"],"mesh_terms":[],"keywords":["Inflection point","Quartic plane curve","Mathematics","Plane curve","Quartic function","Inflection","Degree (music)","Plane (geometry)","Point (geometry)","Jordan curve theorem","Geometry","Mathematical analysis","Pure mathematics","Physics","Computer science","Plane and space curves","Plane curves","Mathematics(all)","Mathematics - Algebraic Geometry","FOS: Mathematics","Algebraic Geometry (math.AG)","14H50"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-22T18:00:56.232464Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}