Experiments with Gorenstein Liaison

Liaison Addition and the Structure of a Gorenstein Liaison Class

We study the concept of liaison addition for codimension two subschemes of an arithmetically Gorenstein projective scheme. We show how it relates to liaison and biliaison classes of subschemes and use it to investigate the structure of Gorenstein liaison equivalence classes, extending the known theory for complete intersection liaison of codimension two subschemes. In particular, we show that o...

Liaison Classes of Modules

We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known for Gorenstein liaison are still true in the more general case of module liaison. In particular, we construct two maps from the set of even li...

Some Examples of Gorenstein Liaison in Codimension Three

Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison o varieties of codimension 2 in projective space. In this paper we study points in P and cuves in P in an attempt to see how far typical codimension 2 results will extend. While the results are satisfactory for small degree, we find in each case examples where we cannot dec...

Gorenstein Liaison via Divisors

Gorenstein Algebras Presented by Quadrics

We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a number of different techniques, including liaison theory and generic initial ideals.