Lines in P3

Moduli
The moduli space of lines is P3 is isomorphic to the Grassmannian of 2-dimensional subspaces of C4, G|G(2,4).

Enumerative geometry

 * Through any two distinct points in P3, there is a unique line.
 * Fix two general lines and one general point in P3: there is a unique line intersecting them all.
 * Fix four general lines in P3: there are exactly two lines that intersect all four.

Generalizations

 * Space curves
 * Lines in projective space