On the linearity of the syzygies of Hibi rings

Dharm Veer

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arXiv · 2108.03915

On the linearity of the syzygies of Hibi rings

Dharm Veer

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Abstract

In this article, we prove necessary conditions for Hibi rings to satisfy Green-Lazarsfeld property $N_p$ for $p=2$ and $3$. We also show that if a Hibi ring satisfies property $N_4$, then it is a polynomial ring or it has a linear resolution. Therefore, it satisfies property $N_p$ for all $p\geq 4$ as well. As a consequence, we characterize distributive lattices whose comparability graph is chordal in terms of the subposet of join-irreducibles of the distributive lattice. Moreover, we characterize complete intersection Hibi rings.

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Dharm Veer. 2021-08-09. On the linearity of the syzygies of Hibi rings. https://arxiv.org/abs/2108.03915

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