{"paper":{"title":"On projections of smooth and nodal plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Serge Lvovski, Yu. Burman","submitted_at":"2013-11-08T08:56:57Z","abstract_excerpt":"Suppose that $C\\subset\\mathbb P^2$ is a general enough nodal plane curve of degree $>2$, $\\nu\\colon \\hat C\\to C$ is its normalization, and $\\pi\\colon \\hat C\\to\\mathbb P^1$ is a finite morphism simply ramified over the same set of points as a projection $\\mathrm{pr}_p\\circ \\nu\\colon\\hat C \\to\\mathbb P^1$, where $p\\in\\mathbb P^2\\setminus C$ (if $\\mathrm{deg}\\, C=3$, one should assume in addition that $\\deg\\pi\\ne4$). We prove that the morphism $\\pi$ is equivalent to such a projection if and only if it extends to a finite morphism $X\\to(\\mathbb P^2)^*$ ramified over $C^*$, where $X$ is a smooth su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1904","kind":"arxiv","version":3},"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"}