{"paper":{"title":"L\\^e numbers and Newton diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adam R\\'o\\.zycki, Christophe Eyral, Grzegorz Oleksik","submitted_at":"2018-12-03T09:17:11Z","abstract_excerpt":"We give an algorithm to compute the L\\^e numbers of (the germ of) a Newton non-degenerate complex analytic function $f\\colon(\\mathbb{C}^n,0) \\rightarrow (\\mathbb{C},0)$ in terms of certain invariants attached to the Newton diagram of the function $f+z_1^{\\alpha_1}+\\cdots +z_d^{\\alpha_d}$, where $d$ is the dimension of the critical locus of $f$ and $\\alpha_1,\\ldots, \\alpha_d$ are sufficiently large integers. This is a version for non-isolated singularities of a famous theorem of A. G. Kouchnirenko. As a corollary, we obtain that Newton non-degenerate functions with the same Newton diagram have "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00614","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"}