{"paper":{"title":"A Remark on Classical Pluecker's formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Vik.S. Kulikov","submitted_at":"2011-01-26T12:46:06Z","abstract_excerpt":"For any reduced curve $C\\subset \\mathbb P^2$, we define the notions of the number of its virtual cusps $c_v$ and the number of its virtual nodes $n_v$ which are non-negative, coincide respectively with the numbers of ordinary cusps and nodes in the case of cuspidal curves, and if $\\hat C$ is the dual curve of an irreducible curve $C$ and $\\hat n_v$ and $\\hat c_v$ are the numbers of its virtual nodes and virtual cusps, then the integers $c_v$, $n_v$, $\\hat c_v$, $\\hat n_v$ satisfy Classical Pl\\\"{u}cker's formulae."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5042","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"}