On the Resiliency of Determinantal Ideals

Abstract

Determinantal ideals associated to “sufficiently general” matrices of linear forms are shown to be resilient in the sense that they remain of the “expected” codimension, or prime, even modulo a certain number of linear forms.

This paper is intended to be read as an introduction to the paper Eisenbud [1985], in which a number of further results, and analogues for lower order minors, are treated. We have however included here the material necessary for the construction of Maximal Cohen–Macaulay modules by Herzog and Kühl (elsewhere in these proceedings) and for some other applications to the construction of compressed or nearly compressed algebras and modules.