Binomial edge ideals and rational normal scrolls

Faryal Chaudhry; Ahmet Dokuyucu; Viviana Ene

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arXiv · 1404.7602

Binomial edge ideals and rational normal scrolls

Faryal Chaudhry·Ahmet Dokuyucu·Viviana Ene

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Abstract

Let $X$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaulay. We find the minimal primes of $I_G$ and show that $I_G$ is a set theoretical complete intersection. Moreover, a sharp upper bound for the regularity of $I_G$ is given.

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Faryal Chaudhry, Ahmet Dokuyucu, Viviana Ene. 2014-04-30. Binomial edge ideals and rational normal scrolls. https://arxiv.org/abs/1404.7602

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