  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.
