  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.
