2012/05/14 by Fouli, Louiza, Lin, Kuei-Nuan
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1205.3127
We study the defining equations of the Rees algebra of square-free monomial ideals in a polynomial ring over a field. We determine that when an ideal I is generated by n square-free monomials of the same degree then I has relation type at most n-2 as long as n ≤ 5. In general, we establish the defining equations of the Rees algebra in this case. Furthermore, we give a class of examples with relation type at least n-2, where n=μ(I). We also provide new classes of ideals of linear type. We propose the construction of a graph, namely the generator graph of an ideal, where the monomial generators serve as vertices for the graph. We show that when I is a square-free monomial ideal generated in the same degree that is at least 2 and the generator graph of I is the graph of a disjoint union of trees and graphs with unique odd cycles then I is an ideal of linear type.