Graded ideals of König type

Herzog, Jürgen; Hibi, Takayuki; Moradi, Somayeh

doi:10.1090/tran/8531

Graded ideals of König type
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by Jürgen Herzog, Takayuki Hibi and Somayeh Moradi PDF

Trans. Amer. Math. Soc. 375 (2022), 301-323 Request permission

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 $in_<(I)$ 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 $in_<(I)$, 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.

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