{"paper":{"title":"Le tissu dual d'un pr\\'e-feuilletage convexe r\\'eduit sur $\\mathbb{P}^{2}_{\\mathbb{C}}$ est plat","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Samir Bedrouni","submitted_at":"2024-11-20T12:05:09Z","abstract_excerpt":"A holomorphic pre-foliation $\\mathscr{F}=\\mathcal{C}\\boxtimes\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$ is the data of a reduced complex projective curve $\\mathcal{C}$ of $\\mathbb{P}^{2}_{\\mathbb{C}}$ and a holomorphic foliation $\\mathcal{F}$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$. When the foliation $\\mathcal{F}$ is convex (resp. reduced convex) and the curve $\\mathcal{C}$ is invariant by $\\mathcal{F}$, we say that the pre-foliation $\\mathscr{F}=\\mathcal{C}\\boxtimes\\mathcal{F}$ is convex (resp. reduced convex). We prove that the dual web of a reduced convex pre-foliation on $\\mathbb{P}^{2}_{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13246","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13246/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}