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.