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arXiv · 1403.5769

On a generic symmetry defect hypersurface

S. Janeczko·Z. Jelonek·M. A. S. Ruas
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Abstract

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.

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S. Janeczko, Z. Jelonek, M. A. S. Ruas. 2014-03-23. On a generic symmetry defect hypersurface. https://arxiv.org/abs/1403.5769

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