{"paper":{"title":"Feuilletages de degr\\'e trois du plan projectif complexe ayant une transform\\'ee de Legendre plate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Samir Bedrouni","submitted_at":"2017-12-11T17:15:32Z","abstract_excerpt":"The set $\\mathbf{F}(d)$ of foliations of degree $d$ on the complex projective plane can be identified with a Zariski's open set of a projective space of dimension $(d+2)^2-2$ on which acts $\\mathrm{Aut}(\\mathbb{P}^{2}_{\\mathbb{C}})$. The subset $\\mathbf{FP}(d)$ of $\\mathbf{F}(d)$ consisting of foliations of $\\mathbf{F}(d)$ with a flat Legendre transform (dual web) is a Zariski closed subset of $\\mathbf{F}(d)$. In this dissertation we study foliations of $\\mathbf{FP}(d)$ and we try to better understand the topological structure of $\\mathbf{FP}(3)$. First, we establish some effective criteria fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03895","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}