Rigid monomial ideals

Timothy B.P. Clark, Sonja Mapes

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

In this paper we investigate the class of rigid monomial ideals and characterize them by the fact that their minimal resolution has a unique Zd-graded basis. Furthermore, we show that certain rigid monomial ideals are lattice-linear, so their minimal resolution can be constructed as a poset resolution. We then give a description of the minimal resolution of a larger class of rigid monomial ideals by appealing to the structure of L(n), the lattice of all lcmlattices of monomial ideals on n generators. By xing a stratum in L(n) where all ideals have the same total Betti numbers, we show that rigidity is a property which propagates upward in L(n). This allows the minimal resolution of any rigid ideal contained in a xed stratum to be constructed by relabeling the resolution of a rigid monomial ideal whose resolution has been constructed by other methods.

Original languageEnglish (US)
Pages (from-to)33-52
Number of pages20
JournalJournal of Commutative Algebra
Volume6
Issue number1
DOIs
StatePublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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