{"paper":{"title":"Milnor Fibrations and the Thom Property for maps $f \\bar g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anne Pichon, Jos\\'e Seade","submitted_at":"2011-03-16T17:20:42Z","abstract_excerpt":"We prove that every map-germ ${f \\bar g}: (\\C^n,\\0) {\\to}(\\C,0)$ with an isolated critical value at 0 has the Thom $a_{f \\bar g}$-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs $f \\bar g$ and it implies that every such map-germ has a Milnor-L\\^e fibration defined on a Milnor tube. One thus has a locally trivial fibration $\\phi: \\mathbb S_\\e \\setminus K \\to \\mathbb S^1$ for every sufficiently small sphere around $\\0$, where $K$ is the link of $f \\bar g$ and in a neighbourhood of $K$ the projection map $\\phi$ is given by $f \\bar g / | f \\bar g|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3236","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"}