Rees algebras of square-free monomial ideals

Louiza Fouli, Kuei Nuan Lin

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)25-54
Number of pages30
JournalJournal of Commutative Algebra
Volume7
Issue number1
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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