The eventual shape of Betti tables of powers of ideals

2011/10/03 by Amir Bagheri, Bagheri, Amir, Marc Chardin +3
Computer Science · Mathematics · #13D02 #13D45 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1110.0383

openalex publication_date 2011/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finitely generated abelian group, and let S = A[x₁, ..., x_n] be a G-graded polynomial ring over a commutative ring A. Let I₁, ..., I_s be G-homogeneous ideals in S, and let M be a finitely generated G-graded S-module. We show that, when A is Noetherian, the nonzero G-graded Betti numbers of MI₁^t₁ ... I_s^t_s exhibit an asymptotic linear behavior as the t_is get large.

Citations

• Stabilization of the Regularity of Powers of An Ideal

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