Mathematical Research Letters

Volume 20 (2013)

Number 6

The eventual shape of Betti tables of powers of ideals

Pages: 1033 – 1046

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n6.a3

Authors

Bagheri Amir (Institut de Mathématiques de Jussieu, UPMC, Paris, France)

Chardin Marc (Institut de Mathématiques de Jussieu, UPMC, Paris, France)

Huy Tài Hà (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Abstract

Let $G$ be an abelian group and $S$ be a $G$-graded a Noetherian algebra over a commutative ring $A \subseteq S_0$. Let $I_1, \dots, I_s$ be $G$-homogeneous ideals in $S$, and let $M$ be a finitely generated $G$-graded $S$-module. We show that the shape of non-zero $G$-graded Betti numbers of $MI_1^{t_1} \cdots I_s^{t_s}$ exhibit an eventual linear behavior as the $t_i$s get large.

Keywords

Betti numbers, asymptotic linearity, multigraded

2010 Mathematics Subject Classification

13D02, 13D45

Full Text (PDF format)