{"paper":{"title":"Computing the Singularities of Rational Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"C. Villarino, J.R. Sendra, S. Perez-Diaz","submitted_at":"2011-07-26T16:36:34Z","abstract_excerpt":"Given a rational projective parametrization $\\cP(\\ttt,\\sss,\\vvv)$ of a rational projective surface $\\cS$ we present an algorithm such that, with the exception of a finite set (maybe empty) $\\cB$ of projective base points of $\\cP$, decomposes the projective parameter plane as $\\projdos\\setminus \\cB=\\cup_{k=1}^{\\ell} \\cSm_k$ such that if $(\\ttt_0:\\sss_0:\\vvv_0)\\in \\cSm_k$ then $\\cP(\\ttt_0,\\sss_0,\\vvv_0)$ is a point of $\\cS$ of multiplicity $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5262","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"}