{"paper":{"title":"On the holomorphy of the curvature of planar webs along an invariant curve","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.DS","authors_text":"Samir Bedrouni","submitted_at":"2026-06-11T13:57:11Z","abstract_excerpt":"Let $\\mathcal{W}=\\mathcal{W}_{n}\\boxtimes\\mathcal{W}_{d-n}$ be a $d$-web on $(\\mathbb{C}^2,0)$, where $\\mathcal{W}_n$ is an $n$-web with a totally invariant irreducible curve~$C$, and $\\mathcal{W}_{d-n}$ is a regular $(d-n)$-web transverse to $C$. We show that the curvature of $\\mathcal{W}$ is holomorphic along $C$ if and only if the curvature of $\\mathcal{W}_n$ is holomorphic along $C$. When $\\mathcal{W}_n$ is non-degenerate along $C$, we prove that $K(\\mathcal{W}_n)$, and hence $K(\\mathcal{W})$, is holomorphic along $C.$ We deduce that, if $\\mathcal{W}_n$ is irreducible and $\\mathrm{mult}\\le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13373","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13373/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"}