Splittings of toric ideals

JOURNAL OF ALGEBRA

卷:574

Article

Favacchio, Giuseppe¹  Hofscheier, Johannes²  Keiper, Graham³  Van Tuyl, Adam³ 

[1] Politecn Torino, DISMA Dept Math Sci, Turin, Italy

[2] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

[3] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4L8, Canada

关键词: Toric ideals;    Graphs;    Graded Betti numbers;   

DOI  :  10.1016/j.jalgebra.2021.01.012

来源: Elsevier

【 摘 要 】

Let I subset of R= K[x(1),..., x(n)] be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal Ican be split into the sum of two smaller toric ideals. For a general toric ideal I, we give a sufficient condition for this splitting in terms of the integer matrix that defines I. When I= I-G is the toric ideal of a finite simple graph G, we give additional splittings of IGrelated to subgraphs of G. When there exists a splitting I = I-1+ I-2 of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of Iin terms of the (multi-)graded Betti numbers of I-1 and I-2. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free