{"paper":{"title":"A note on the plane curve singularities in positive characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arkadiusz P{\\l}oski, Evelia R. Garc\\'ia Barroso","submitted_at":"2022-07-29T07:45:08Z","abstract_excerpt":"Given an algebroid plane curve $f=0$ over an algebraically closed field of characteristic $p\\geq 0$ we consider the Milnor number $\\mu(f)$, the delta invariant $\\delta(f)$ and the number $r(f)$ of its irreducible components. Put $\\bar \\mu(f)=2\\delta(f)-r(f)+1$. If $p=0$ then $\\bar \\mu (f)=\\mu(f)$ (the Milnor formula). If $p>0$ then $\\mu(f)$ is not an invariant and $\\bar \\mu(f)$ plays the role of $\\mu(f)$. Let $\\mathcal N_f$ be the Newton polygon of $f$. We define the numbers $\\mu(\\mathcal N_{f})$ and $r(\\mathcal N_{f})$ which can be computed by explicit formulas. The aim of this note is to giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.14523","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.14523/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}