{"paper":{"title":"Incidences between points on a variety and planes in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Micha Sharir, Noam Solomon","submitted_at":"2016-03-15T19:10:22Z","abstract_excerpt":"In this paper we establish an improved bound for the number of incidences between a set $P$ of $m$ points and a set $H$ of $n$ planes in $\\mathbb R^3$, provided that the points lie on a two-dimensional nonlinear irreducible algebraic variety $V$ of constant degree. Specifically, the bound is $$ O\\left( m^{2/3}n^{2/3} + m^{6/11}n^{9/11}\\log^\\beta(m^3/n) + m + n + \\sum_\\ell |P_\\ell|\\cdot |H_\\ell| \\right) , $$ where the constant of proportionality and the constant exponent $\\beta$ depend on the degree of $V$, and where the sum ranges over all lines $\\ell$ that are fully contained in $V$ and conta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04823","kind":"arxiv","version":2},"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"}