Full paper in PDF:
$% J. Huisman, Real cubic hypersurfaces and group laws, Rev. Mat. Complut. 17
(2004), 395–401.%$
Real Cubic Hypersurfaces and Group Laws
Let be a real cubic hypersurface in
. Let
be the pseudo-hyperplane
of
, i.e.,
is the irreducible global real analytic branch of the
real analytic variety
such that the homology class
is nonzero
in
. Let
be the set of real linear subspaces
of
of dimension
contained in
such that
. We show that,
under certain conditions on
, there is a group law on the set
. It
is determined by
in
if and only if there is a real
hyperplane
in
such that
. We also study the
case when these conditions on
are not satisfied.
Key words: real cubic hypersurface, real cubic curve, real cubic surface,
pseudo-hyperplane, pseudo-line, pseudo-plane, linear subspace, group.
2000 Mathematics Subject Classification: 14J70, 14P25.