Ideals of Adjacent Minors
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
We give a description of the minimal primes of the ideal generated by the 2 x 2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m x m minors of an m x n generic matrix when the characteristic of the ground field is zero. A key intermediate result is the proof that the ideals which appear as minimal primes are, in fact, prime ideals. This introduces a large new class of mixed determinantal ideals that are prime.
Cite
@article{arxiv.math/0306318,
title = {Ideals of Adjacent Minors},
author = {Serkan Hosten and Seth Sullivant},
journal= {arXiv preprint arXiv:math/0306318},
year = {2007}
}