  We investigate Rees algebras and special fiber rings obtained by blowing up
specialized Ferrers ideals. This class of monomial ideals includes strongly
stable monomial ideals generated in degree two and edge ideals of prominent
classes of graphs. We identify the equations of these blow-up algebras. They
generate determinantal ideals associated to subregions of a generic symmetric
matrix, which may have holes. Exhibiting Gr\"obner bases for these ideals and
using methods from Gorenstein liaison theory, we show that these determinantal
rings are normal Cohen-Macaulay domains that are Koszul, that the initial
ideals correspond to vertex decomposable simplicial complexes, and we determine
their Hilbert functions and Castelnuovo-Mumford regularities. As a consequence,
we find explicit minimal reductions for all Ferrers and many specialized
Ferrers ideals, as well as their reduction numbers. These results can be viewed
as extensions of the classical Dedekind-Mertens formula for the content of the
product of two polynomials.
