NEW CONSTRUCTION OF THE EAGON-NORTHCOTT COMPLEX

Abstract

The authors [6] introduced the concept of a complete matrix of grade g > 3 to describe a structure theorem for complete intersections of grade g > 3. We show that a complete matrix can be used to construct the Eagon-Northcott complex [7]. Moreover, we prove that it is the minimal free resolution F of a class of deter- minantal ideals of n × (n + 2) matrices X = (x_{ij} ) such that entries of each row of X = (x_{ij}) form a regular sequence and the second differential map of F is a matrix f defined by the complete matrices of grade n + 2.