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arXiv · 1904.04499

Almost complete intersection binomial edge ideals and their Rees algebras

A. V. Jayanthan·Arvind Kumar·Rajib Sarkar
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Abstract

Let $G$ be a simple graph on $n$ vertices and $J_G$ denote the binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the second graded Betti numbers of $J_G$, and we obtain a minimal presentation of it when $G$ is a tree or a unicyclic graph. We classify all graphs whose binomial edge ideals are almost complete intersection, prove that they are generated by a $d$-sequence and that the Rees algebra of their binomial edge ideal is Cohen-Macaulay. We also obtain an explicit description of the defining ideal of the Rees algebra of those binomial edge ideals.

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A. V. Jayanthan, Arvind Kumar, Rajib Sarkar. 2019-04-09. Almost complete intersection binomial edge ideals and their Rees algebras. https://arxiv.org/abs/1904.04499

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