Illinois Journal of Mathematics

Generalized divisors and biliaison

Robin Hartshorne

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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.

Article information

Illinois J. Math., Volume 51, Number 1 (2007), 83-98.

First available in Project Euclid: 20 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 14M06: Linkage [See also 13C40]


Hartshorne, Robin. Generalized divisors and biliaison. Illinois J. Math. 51 (2007), no. 1, 83--98. doi:10.1215/ijm/1258735326.

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