Generalized Divisors and Biliaison

Details Generalized Divisors and Biliaison Generalized Divisors and Biliaison

2003-01-15

arxiv.org/abs/math/0301162v2

Mathematics

Algebraic Geometry

15 pages. A new section 5 with a new theorem has been added to the paper

Scientific paper

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.

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