{"paper":{"title":"The Coolidge-Nagata conjecture, part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Karol Palka","submitted_at":"2014-05-22T21:49:39Z","abstract_excerpt":"Let $E\\subseteq \\mathbb{P}^2$ be a complex rational cuspidal curve contained in the projective plane and let $(X,D)\\to (\\mathbb{P}^2,E)$ be the minimal log resolution of singularities. Applying the log minimal model program to $(X,\\frac{1}{2}D)$ we prove that if $E$ has more than two singular points or if $D$, which is a tree of rational curves, has more than six maximal twigs or if $\\mathbb{P}^2\\setminus E$ is not of log general type then $E$ is Cremona equivalent to a line, i.e. the Coolidge-Nagata conjecture for $E$ holds. We show also that if $E$ is not Cremona equivalent to a line then th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5917","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"}