Cohen-Macaulay binomial edge ideals

We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen--Macaulay.Comment: 9 page

Binomial edge ideals and rational normal scrolls

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

A note on the regularity of Hibi rings

We compute the regularity of the Hibi ring of any finite distributive lattice in terms of its poset of join irreducible elements.Comment: 5 pages, 2 figure