  This article shows that for generic choice of Riemannian metric on a smooth
manifold $M$ of dimension four, all prime compact parametrized minimal surfaces
within $M$ have self-intersections in general position in the following sense:
self-intersections are transverse and the two tangent planes at any
self-intersection point fail to be complex with respect to any orthogonal
complex structure on the ambient manifold $M$. This implies via a result of
Sheldon Chang that $H_2(M;{\mathbb Z})$ is generated by homology classes that
are represented by imbedded minimal surfaces.
