Hyperplanes in projective space

A hyperplane in Pn is the linear subspace defined by a homogeneous polynomial of degree 1.

Moduli
The moduli space of hyperplanes in Pn is naturally isomorphic to the dual Pn, via the map that sends a hyperplane to the defining polynomial (up to scaling).

Special cases

 * Lines in P2
 * Planes in P3

Generalizations

 * Hypersurfaces in projective space
 * Linear subspaces in projective space