{"paper":{"title":"Classification of foliations of degree three on $\\mathbb{P}^{2}_{\\mathbb{C}}$ with a flat Legendre transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"David Mar\\'in, Samir Bedrouni","submitted_at":"2018-03-22T18:10:00Z","abstract_excerpt":"The set $\\mathbf{F}(3)$ of foliations of degree three on the complex projective plane can be identified with a Zariski's open set of a projective space of dimension $23$ on which acts $\\mathrm{Aut}(\\mathbb{P}^{2}_{\\mathbb{C}})$. The subset $\\mathbf{FP}(3)$ of $\\mathbf{F}(3)$ consisting of foliations of $\\mathbf{F}(3)$ with a flat Legendre transform (dual web) is a Zariski closed subset of $\\mathbf{F}(3)$. We classify up to automorphism of $\\mathbb{P}^{2}_{\\mathbb{C}}$ the elements of $\\mathbf{FP}(3)$. More precisely, we show that up to automorphism there are $16$ foliations of degree three wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08526","kind":"arxiv","version":2},"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"}