{"paper":{"title":"Doubling coverings of algebraic hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Omer Friedland, Yosef Yomdin","submitted_at":"2015-12-09T15:35:32Z","abstract_excerpt":"A doubling covering $\\U$ of a complex $n$-dimensional manifold $Y$ consists of analytic functions $\\psi_j:B_1\\to Y$, each function being analytically extendable, as a mapping to $Y$, to a four times larger concentric ball $B_4$.\n  Main result of this paper is an upper bound on the minimal number $\\kappa({\\U})$ of charts in doubling coverings of a manifold $Y$, being a compact part of a non-singular level hypersurface $Y=\\{P=c\\}$, where $P$ is a polynomial on $\\C^n$ with non-degenerated critical points. We show that $\\kappa({\\U})$ is of order $\\log({1}/{\\rho})$, where $\\rho$ is the distance fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02903","kind":"arxiv","version":3},"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"}