High Quality Content by WIKIPEDIA articles! In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n ? 1 dimensions is a hypersurface. Equivalently, the codimension of a hypersurface is one. In algebraic geometry, a hypersurface in projective space of dimension n is an algebraic set that is purely of dimension n ? 1. It is then defined by a single equation F = 0, a homogeneous polynomial in the homogeneous coordinates. It may have singularities, so not in fact be a submanifold in the strict sense. "Primal" is an old term for an irreducible hypersurface.

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