Graded ideals of König type

Abstract

Inspired by the notion of König graphs we introduce graded ideals of König type with respect to a monomial order $<$. It is shown that if $I$ is of König type, then the Cohen--Macaulay property of $\ini_<(I)$ does not depend on the characteristic of the base field. This happens to be the case also for $I$ itself when $I$ is a binomial edge ideal. Attached to an ideal of König type is a sequence of linear forms, whose elements are variables or differences of variables. This sequence is a system of parameters for $\ini_<(I)$, and is a potential system of parameters for $I$ itself. We study in detail the ideals of König type among the edge ideals, binomial edge ideals and the toric ideal of a Hibi ring and use the König property to determine explicitly their canonical module.

References in corpus (1)

• Cohen-Macaulay binomial edge ideals and accessible graphs