{"paper":{"title":"Unlikely Intersection For Two-Parameter Families of Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Dragos Ghioca, Liang-Chung Hsia, Thomas J. Tucker","submitted_at":"2015-07-17T15:11:29Z","abstract_excerpt":"Let $c_1, c_2, c_3$ be distinct complex numbers, and let $d\\ge 3$ be an integer. We show that the set of all pairs $(a,b)\\in \\mathbb{C}\\times \\mathbb{C}$ such that each $c_i$ is preperiodic for the action of the polynomial $x^d+ax+b$ is not Zariski dense in the affine plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04993","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"}