{"paper":{"title":"Primitive normal completions of the affine plane II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pinaki Mondal","submitted_at":"2011-10-31T19:42:04Z","abstract_excerpt":"In this article we continue from \\cite{sub2-1} the study of normal analytic compactifications of $\\cc^2$ from the point of view of their associated pencils of jets of curve germs centered at infinity. If $\\bar X$ is a normal analytic compactification of $\\cc^2$ which is {\\em primitive}, i.e.\\ $\\bar X \\setminus \\cc^2$ is irreducible curve, then we show that $\\bar X$ is projective iff $\\bar X$ is algebraic iff at least one of the jets in the associated pencil of jets of curve-germs can be represented by a planar curve with one place at infinity. As a result we show that there are primitive norma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6914","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"}