  A smooth, compact 4-manifold with a Riemannian metric and b^(2+) > 0 has a
non-trivial, closed, self-dual 2-form. If the metric is generic, then the zero
set of this form is a disjoint union of circles. On the complement of this zero
set, the symplectic form and the metric define an almost complex structure; and
the latter can be used to define pseudo-holomorphic submanifolds and
subvarieties. The main theorem in this paper asserts that if the 4-manifold has
a non zero Seiberg-Witten invariant, then the zero set of any given self-dual
harmonic 2-form is the boundary of a pseudo-holomorphic subvariety in its
complement.
