  These are notes on some algebraic geometry of complex projective curves,
together with an application to studying the contact curves in CP^3 and the
null curves in the complex quadric Q^3 in CP^4, related by the well-known Klein
correspondence. Most of this note consists of recounting the classical
background. The main application is the explicit classification of rational
null curves of low degree in Q^3.
  I have recently received a number of requests for these notes, so I am
posting them to make them generally available.
