{"paper":{"title":"Classification of planar rational cuspidal curves. I. C**-fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Karol Palka, Tomasz Pe{\\l}ka","submitted_at":"2016-09-13T19:34:02Z","abstract_excerpt":"To classify complex rational cuspidal curves $E\\subseteq \\mathbb{P}^2$ it remains to classify the ones with complement of log general type, i.e. the ones for which $\\kappa(K_X+D)=2$, where $(X,D)$ is a log resolution of $(\\mathbb{P}^2,E)$. It is conjectured that $\\kappa(K_X+\\frac{1}{2}D)=-\\infty$ and hence $\\mathbb{P}^2\\setminus E$ is $\\mathbb{C}^{**}$-fibered, where $\\mathbb{C}^{**}=\\mathbb{C}^1\\setminus\\{0,1\\}$, or $-(K_X+\\frac{1}{2}D)$ is ample on some minimal model of $(X,\\frac{1}{2}D)$. Here we classify, up to a projective equivalence, those rational cuspidal curves for which the compleme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03992","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"}