{"paper":{"title":"On Normal Forms of Singular Levi-Flat Real Analytic Hypersurfaces","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Arturo Fern\\'andez-P\\'erez","submitted_at":"2010-03-25T20:58:19Z","abstract_excerpt":"Let $F(z)=\\mathcal{R}e(P(z)) + h.o.t$ be such that $M=(F=0)$ defines a germ of real analytic Levi-flat at $0\\in\\mathbb{C}^{n}$, $n\\geq{2}$, where $P(z)$ is a homogeneous polynomial of degree $k$ with an isolated singularity at $0\\in\\mathbb{C}^{n}$ and Milnor number $\\mu$. We prove that there exists a holomorphic change of coordinate $\\phi$ such that $\\phi(M)=(\\mathcal{R}e(h)=0)$ where $h(z)$ is a polynomial of degree $\\mu+1$ and $j^{k}_{0}(h)=P$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4999","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":""},"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"}