{"paper":{"title":"Doubling coverings via resolution of singularities and preparation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO"],"primary_cat":"math.CA","authors_text":"Omer Friedland, Raf Cluckers, Yosef Yomdin","submitted_at":"2019-03-11T13:12:57Z","abstract_excerpt":"In this paper we provide asymptotic upper bounds on the complexity in two (closely related) situations. We confirm for the total doubling coverings and not only for the chains the expected bounds of the form $$ \\kappa({\\mathcal U}) \\le K_1(\\log ({1}/{\\delta}))^{K_2} . $$ This is done in a rather general setting, i.e. for the $\\delta$-complement of a polynomial zero-level hypersurface $Y_0$ and for the regular level hypersurfaces $Y_c$ themselves with no assumptions on the singularities of $P$. The coefficient $K_2$ is the ambient dimension $n$ in the first case and $n-1$ in the second case. Ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04281","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":""},"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"}