Space curves

Any smooth abstract curve can be embedded in P3 by first embedding it in some large-dimensional projective space via an ample line bundle, then projecting away from a linear subspace that misses the curve's 3-dimensional secant variety.

Special cases

 * Lines in P3
 * Conics in P3
 * Twisted cubic curves

Generalizations

 * Curves in projective space
 * Codimension 2 subvarieties in projective space