  We introduce the notion of the projective linking number Link(M,Z) of a
compact oriented real submanifold M of dimension 2p-1 in complex projective
n-space P^n with an algebraic subvariety Z in P^n - M of codimension p. This
notion is related to projective winding numbers and quasi-plurisubharmonic
functions, and it generalizes directly from P^n to any projective manifold.
Part 1 of this paper establishes the following result for the case p=1. Let M
be an oriented, stable, real analytic curve in P^n. Then M is the boundary of a
positive holomorphic 1-chain T with Mass(T) < K in P^n if and only if Link(M,Z)
> -K deg(Z) for all algebraic hypersurfaces Z in P^n - M.
  An analogous theorem is implied in any projective manifold. Part 2 of this
paper studies similar results for p>1.
