{"paper":{"title":"Asymptotic equisingularity and topology of complex hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mihai Tibar","submitted_at":"1998-05-18T09:09:40Z","abstract_excerpt":"We consider an equisingularity problem for polynomial families of affine hypersurfaces $X_\\tau \\subset \\mathbb C^n$ with (at worst) isolated singularities. We show that the constancy of the global polar invariants $\\gamma^* (X_\\tau)$ is equivalent to the $t$-equisingularity at infinity, an asymptotic-type equisingularity that we introduce. We prove that $\\gamma^*$-constancy implies C$^\\infty$-triviality in the neighbourhood of infinity. We show how the invariants $\\gamma^*$ enter in the description of a CW-complex model of a hypersurface $X_\\tau$ and therefore provide in particular new invaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9805075","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"}