{"paper":{"title":"Arnold's problem on monotonicity of the Newton number for surface singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Justyna Walewska, Szymon Brzostowski, Tadeusz Krasi\\'nski","submitted_at":"2017-04-30T15:14:38Z","abstract_excerpt":"According to the Kouchnirenko theorem, for a generic (precisely non-degenerate in the Kouchnirenko sense) isolated singularity $f$ its Milnor number $\\mu (f)$ is equal to the Newton number $\\nu (\\Gamma_{+}(f))$ of a combinatorial object associated to $f$, the Newton polyhedron $\\Gamma_+ (f)$. We give a simple condition characterising, in terms of $\\Gamma_+ (f)$ and $\\Gamma_+ (g)$, the equality $\\nu (\\Gamma_{+}(f)) = \\nu (\\Gamma_{+}(g))$, for any surface singularities $f$ and $g$ satisfying $\\Gamma_+ (f) \\subset \\Gamma_+ (g)$. This is a complete solution to an Arnold's problem (1982-16) in this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00323","kind":"arxiv","version":2},"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"}