  We deduce results on the dimension and connectedness of degeneracy loci of
maps of finite modules $f:M\to N$ over a local noetherian ring $(A,{\mathfrak
m})$. We show for instance that the expected determinantal bounds on the
dimension of the t-$th$ degeneracy locus of $f$ hold if $f\in {\mathfrak m} Hom
(M,N)$, and that this degeneracy locus is connected in the expected dimension
provided $\hat A$ is a domain.
