  We determine the possible Hilbert functions of graded rank one torsion free
modules over three dimensional Artin-Schelter regular algebras. It turns out
that, as in the commutative case, they are related to Castelnuovo functions.
  From this we obtain an intrinsic proof that the space of torsion free rank
one modules on a non-commutative projective plane is connected. A different
proof of this fact, based on deformation theoretic methods and the known
commutative case has recently been given by Nevins and Stafford. For the Weyl
algebra it was proved by Wilson.
