Betti table Stabilization of Homogeneous Monomial Ideals

2017/12/12 by Slobodin, Aaron
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.04411

Abstract

Given an homogeneous monomial ideal I, we provide a question- and example-based investigation of the stabilization patterns of the Betti tables shapes of I^d as we vary d. We build off Whieldon's definition of the stabilization index of I, Stab(I), to define the stabilization sequence of I, StabSeq(I), and use it to explore changes in the shapes of the Betti tables of I^d as we vary d. We also present the stabilization indices and sequences of the collection of ideals \I_n\ where I_n=(a²ⁿb²ⁿc²ⁿ,b⁴ⁿc²ⁿ,a³ⁿc³ⁿ,a^6n-1b)⊆ \Bbbk[a,b,c].

Related

• Stabilization of Betti Tables
• Decompositions of Betti diagrams of powers of monomial ideals: A stability conjecture
• An alternative algorithm for computing the Betti table of a monomial ideal
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