## Illinois Journal of Mathematics

### Generalized divisors and biliaison

Robin Hartshorne

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 20 November 2009

https://projecteuclid.org/euclid.ijm/1258735326

Digital Object Identifier
doi:10.1215/ijm/1258735326

Mathematical Reviews number (MathSciNet)
MR2346188

Zentralblatt MATH identifier
1133.14005

#### Citation

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