Almost complete intersection binomial edge ideals and their Rees algebras

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Jayanthan, A., V¹  Kumar, Arvind²  Sarkar, Rajib¹ 

[1] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India

[2] Indian Inst Technol, Dept Math, New Delhi 110016, India

关键词: Binomial edge ideal;    Syzygy;    Rees algebra;    Betti number;   

DOI  :  10.1016/j.jpaa.2020.106628

来源: Elsevier

【 摘 要 】

Let G be a simple graph on n vertices and J(G) denote the binomial edge ideal of G in the polynomial ring S = K[x(1) , . . . , x(n), y(1) , . . . , 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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free