{"paper":{"title":"On a generic symmetry defect hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"M.A.S. Ruas, S. Janeczko, Z. Jelonek","submitted_at":"2014-03-23T16:31:49Z","abstract_excerpt":"Let f : X -> Y be a dominant polynomial mapping of affine varieties. For generic y in Y we have Sing(f^{-1}(y)) = f^{-1}(y) \\cap Sing(X): As an application we show that symmetry defect hypersurfaces for two generic members of the irreducible algebraic family of n-dimensional smooth irreducible subvarieties in general position in C^{2n} are homeomorphic and they have homeomorphic sets of singular points. In particular symmetry defect curves for two generic curves in C^2 of the same degree have the same number of singular points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5769","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"}