Seminar

We will review the definition and basic facts about Gorenstein liaison of varieties in projective space. Taking the case of codimension 2, which is well understood, as a paradigm, we will consider the questions that arise in higher codimensions. A major problem is whether every arithmetically Cohen-Macaulay variety is in the Gorenstein liaison class of a complete intersection (in acronyms: does ACM => glicci?). While this has been proved to be so in many particular cases, the problem is open in general. We will examine some known cases and two striking recent results in the hope of clarifying where the difficulty lies.