The eventual shape of the Betti table of \mathfrakm^kM

2023/08/01 by Antonino Ficarra, Jürgen Herzog, Ficarra, Antonino +3
Chemistry · Computer Science · Mathematics · #13D02 #13F20 #13F55 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Synthesis and pharmacology of benzodiazepine derivatives

paper · pdf · doi:10.48550/arxiv.2308.00639

openalex publication_date 2023/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be the polynomial ring over a field K in a finite set of variables, and let \mathfrakm be the graded maximal ideal of S. It is known that for a finitely generated graded S-module M and all integers k≫ 0, the module \mathfrakm^kM is componentwise linear. For large k we describe the pattern of the Betti table of \mathfrakm^kM when char(K)=0 and M is a submodule of a finitely generated graded free S-module. Moreover, we show that for any k≫ 0, \mathfrakm^kI has linear quotients if I is a monomial ideal.

Related

• Betti tables of monomial ideals fixed by permutations of the variables
• The eventual shape of Betti tables of powers of ideals
• The graded Betti numbers of truncation of ideals in polynomial rings
• Squarefree monomial modules and extremal Betti numbers
• Monomial ideals with large projective dimension