{"paper":{"title":"Singularities of plane rational curves via projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Alessandro Gimigliano, Monica Id\\`a","submitted_at":"2016-09-07T08:37:29Z","abstract_excerpt":"We consider the parameterization ${\\mathbf{f}}=(f_0,f_1,f_2)$ of a plane rational curve $C$ of degree $n$, and we want to study the singularities of $C$ via such parameterization. We do this by using the projection from the rational normal curve $C_n\\subset \\mathbb{P}^n$ to $C$ and its interplay with the secant varieties to $C_n$. In particular, we define via ${\\mathbf{f}}$ certain 0-dimensional schemes $X_k\\subset \\mathbb{P}^k$, $2\\leq k\\leq (n-1)$, which encode all information on the singularities of multiplicity $\\geq k$ of $C$ (e.g. using $X_2$ we can give a criterion to determine whether "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01877","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"}