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Real cubic hypersurfaces and group laws.

Johannes Huisman — 2004

Revista Matemática Complutense

Let X be a real cubic hypersurface in P. Let C be the pseudo-hyperplane of X, i.e., C is the irreducible global real analytic branch of the real analytic variety X(R) such that the homology class [C] is nonzero in H(P(R),Z/2Z). Let be the set of real linear subspaces L of P of dimension n - 2 contained in X such that L(R) ⊆ C. We show that, under certain conditions on X, there is a group law on the set . It is determined by L + L' + L = 0 in if and only if there is a real hyperplane H in P such...

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