We extend the theory of generalized divisors so as to work on any scheme
$X$ satisfying the condition $S_2$ of Serre. We define a generalized
notion of Gorenstein biliaison for schemes in projective space. With
this we give a new proof in a stronger form of the theorem of Gaeta,
that standard determinantal schemes are in the Gorenstein biliaison
class of a complete intersection.
¶
We also show, for schemes of codimension three in ${\mathbb P}^n$, that
the relation of Gorenstein biliaison is equivalent to the relation of
even strict Gorenstein liaison.