On a generic symmetry defect hypersurface
Algebraic Geometry
2014-03-25 v1
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.
Cite
@article{arxiv.1403.5769,
title = {On a generic symmetry defect hypersurface},
author = {S. Janeczko and Z. Jelonek and M. A. S. Ruas},
journal= {arXiv preprint arXiv:1403.5769},
year = {2014}
}