{"paper":{"title":"The {\\L}ojasiewicz Exponent of Semiquasihomogeneous Singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Computer Science, Poland), Szymon Brzostowski (1) ((1) Faculty of Mathematics, University of \\L\\'od\\'z","submitted_at":"2014-05-20T18:11:46Z","abstract_excerpt":"Let $f: (\\mathbb{C}^n,0) \\rightarrow (\\mathbb{C},0)$ be a semiquasihomogeneous function. We give a formula for the local {\\L}ojasiewicz exponent $\\mathcal{L}_{0}(f)$ of $f$, in terms of weights of $f$. In particular, in the case of a quasihomogeneous isolated singularity $f$, we generalize a formula for $\\mathcal{L}_{0}(f)$ of Krasi\\'nski, Oleksik and P{\\l}oski ([KOP09]) from $3$ to $n$ dimensions. This was previously announced in [TYZ10], but as a matter of fact it has not been proved correctly there, as noticed by the AMS reviewer T. Krasi\\'nski.\n  As a consequence of our result, we get that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5179","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"}