{"paper":{"title":"An embedding of {\\bf C} in {\\bf C}$^2$ with hyperbolic complement","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Gregery T. Buzzard, John Erik Fornaess","submitted_at":"1995-06-20T00:00:00Z","abstract_excerpt":"Let $X$ be a closed, $1$-dimensional, complex subvariety of $\\CC^2$ and let $\\ol{\\BB}$ be a closed ball in $\\CC^2 - X$. Then there exists a Fatou-Bieberbach domain $\\Omega$ with $X \\subseteq \\Omega \\subseteq \\CC^2 - \\ol{\\BB}$ and a biholomorphic map $\\Phi: \\Omega \\ra \\CC^2$ such that $\\CC^2 - \\Phi(X)$ is Kobayashi hyperbolic. As corollaries, there is an embedding of the plane in $\\CC^2$ whose complement is hyperbolic, and there is a nontrivial Fatou-Bieberbach domain containing any finite collection of complex lines."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9506211","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"}