We determine the defining equations of the Rees algebra of an ideal I in the case where I is a square-free monomial ideal such that each connected component of the line graph of the hypergraph corresponding to I has at most 5 vertices. Moreover, we show in this case that the non-linear equations arise from even closed walks of the line graph, and we also give a description of the defining ideal of the toric ring when I is generated by square-free monomials of the same degree. Furthermore, we provide a new class of ideals of linear type. We show that when I is a square-free monomial ideal with any number of generators and the line graph of the hypergraph corresponding to I is the graph of a disjoint union of trees and graphs with a unique odd cycle, then I is an ideal of linear type.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory