  Simple approaches to the proofs of the L^2 Castelnuovo-de Franchis theorem
and the cup product lemma which give new versions are developed. For example,
suppose u and v are two linearly independent closed holomorphic 1-forms on a
bounded geometry connected complete Kaehler manifold X with v in L^2. According
to a version of the L^2 Castelnuovo-de Franchis theorem obtained in this paper,
if u and v are pointwise linearly dependent, then there exists a surjective
proper holomorphic mapping of X onto a Riemann surface for which u and v are
pull-backs. Previous versions required both forms to be in L^2.
