Commutative Algebra Seminar

Title

Annihilators of Koszul homologies

Abstract

In this talk we reveal some connections between Koszul annihilators and residual intersection. After introducing the concepts, we show how sliding depth conditions provide non-trivial annihilators for Koszul homologies. To this end, we present a family of approximation complexes to determine the Koszul annihilators. The main theorem we’ll discuss is the following:

Let (R, m) be a CM local ring of dimension d, I satisfy Sliding Depth, and depth (R/I)>􏰀 d - s-1. Let J = (a : I) be an s-residual intersection and use H_j(a) to denote the j-th Koszul homology module with respect to a minimal generating set of a. Then I annihilates all H_j(a) for j>0. Surprisingly, this result contradicts one of the old (unpublished) results of G. Levin!