{"paper":{"title":"A bound for the Milnor number of plane curve singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arkadiusz P{\\l}oski","submitted_at":"2013-05-22T12:23:13Z","abstract_excerpt":"Let $f=0$ be a plane algebraic curve of degree $d>1$ with an isolated singular point at the origin of the complex plane. We show that the Milnor number $\\mu_0(f)$ is less than or equal to $(d-1)^2-\\left[\\frac{d}{2}\\right]$, unless $f=0$ is a set of $d$ concurrent lines passing through 0. Then we characterize the curves $f=0$ for which $\\mu_0(f)=(d-1)^2-\\left[\\frac{d}{2}\\right]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5102","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"}