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Betti table Stabilization of Homogeneous Monomial Ideals
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Paper
Betti table Stabilization of Homogeneous Monomial Ideals
2017
Overview
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}=(a^{2n}b^{2n}c^{2n},b^{4n}c^{2n},a^{3n}c^{3n},a^{6n-1}b)\\subseteq \\Bbbk[a,b,c]\\).
Publisher
Cornell University Library, arXiv.org
Subject
