Determinantal Facet Ideals
Commutative Algebra
2015-10-09 v2 Combinatorics
Abstract
We consider ideals generated by general sets of -minors of an -matrix of indeterminates. The generators are identified with the facets of an -dimensional pure simplicial complex. The ideal generated by the minors corresponding to the facets of such a complex is called a determinantal facet ideal. Given a pure simplicial complex , we discuss the question when the generating minors of its determinantal facet ideal form a Gr\"obner basis and when is a prime ideal.
Cite
@article{arxiv.1108.3667,
title = {Determinantal Facet Ideals},
author = {Viviana Ene and Juergen Herzog and Takayuki Hibi and Fatemeh Mohammadi},
journal= {arXiv preprint arXiv:1108.3667},
year = {2015}
}