Classes of cut ideals and their Betti numbers

被引：0

作者：

Jürgen Herzog

Masoomeh Rahimbeigi

Tim Römer

机构：

[1] Universität Duisburg-Essen,Fachbereich Mathematik

[2] Universität Osnabrück,Institut für Mathematik

来源：

São Paulo Journal of Mathematical Sciences | 2023年 / 17卷

关键词：

Cut sets; Monomial ideals; Number of generators; Betti numbers; Cohen–Macaulay type; Powers of ideals; Primary 05E40; 13C99; Secondary 13F20; 13H10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study monomial cut ideals associated to a graph G, which are a monomial analogue of toric cut ideals as introduced by Sturmfels and Sullivant. Primary decompositions, projective dimensions, and Castelnuovo–Mumford regularities are investigated if the graph can be decomposed as 0-clique sums and disjoint union of subgraphs. The total Betti numbers of a cycle are computed. Moreover, we classify all Freiman ideals among monomial cut ideals.

引用

页码：172 / 187

页数：15