Ideals generated by adjacent 2-minors
Commutative Algebra
2011-01-11 v3
Abstract
Ideals generated by adjacent 2-minors are studied. First, the problem when such an ideal is a prime ideal as well as the problem when such an ideal possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly a primary decomposition of the radical ideal of an ideal generated by adjacent 2-minors, and challenge the question of classifying all ideals generated by adjacent 2-minors which are radical ideals. Finally, we discuss connectedness of contingency tables in algebraic statistics.
Cite
@article{arxiv.1012.5789,
title = {Ideals generated by adjacent 2-minors},
author = {Juergen Herzog and Takayuki Hibi},
journal= {arXiv preprint arXiv:1012.5789},
year = {2011}
}