{"paper":{"title":"Kouchnirenko type formulas for local invariants of plane analytic curves","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Janusz Gwozdziewicz","submitted_at":"2007-07-23T16:01:42Z","abstract_excerpt":"Let f(x,y)=0 be an equation of plane analytic curve defined in the neighborhood of the origin and let $\\pi:M\\to(\\Cn^2,0)$ be a local toric modification. We give a formula which connects a number of double points \\delta_0(f)$ with a sum $\\sum_p \\delta_p(\\tilde f)$ which runs over all intersection points of the proper preimage of f=0 with the exceptional divisor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3404","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"}