Lines in P2

A line in P2 is the vanishing of a homogenous polynomial of a degree 1.

Enumerative geometry

 * Through any two distinct points in P2, there is a unique line.

Moduli
The moduli space of lines in P2 is naturally isomorphic to the dual P2.

Generalizations

 * Hyperplanes in projective space
 * Linear subspaces of projective space
 * Plane curves