A.4.3 Polar curves
The polar curve of a hypersurface given by a polynomial
with respect to
(we may consider
as a family of
hypersurfaces parametrized by
) is defined as the Zariski
closure of
if this happens to be a curve. Some authors consider
itself as polar curve.
We may consider projective hypersurfaces
affine hypersurfaces
or germs of hypersurfaces
getting in this way
projective, affine or local polar curves.
Now let us compute this for a family of curves. We need the library
elim.lib for saturation and sing.lib for the singular
locus.
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