Abstract
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.
Citation
Robin Hartshorne. "Generalized divisors and biliaison." Illinois J. Math. 51 (1) 83 - 98, Spring 2007. https://doi.org/10.1215/ijm/1258735326
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