Generic graph construction ideals and Greene ’ s theorem

@inproceedings{Bruns1999GenericGC,
title={Generic graph construction ideals and Greene ’ s theorem},
author={Winfried Bruns and Michaĺ Kwieciński},
year={1999}
}

Let X be anm × n matrix of indeterminates, m ≤ n, andT a new indeterminate. Consider the polynomial rings R0 = K[X] andR = R0[T ]. For a given positive integer t ≤ m, consider the ideal It = It(X) generated by thet-minors (i. e. the determinants of the t× t submatrices) of X. Using all these determinantal ideals, we define a new ideal J in R = R0[T ], which we call thegeneric graph construction ideal , as follows: