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Summer 2020 Graded Betti numbers of powers of ideals
Amir Bagheri, Kamran Lamei
J. Commut. Algebra 12(2): 153-169 (Summer 2020). DOI: 10.1216/jca.2020.12.153


Using the concept of vector partition functions, we investigate the asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field. Our main results state that if the polynomial ring is equipped with a positive d -grading, then the Betti numbers of powers of ideals are encoded by finitely many polynomials.

Specially, in the case of -grading, for each homological degree i we can split 2 = { ( μ , t ) t , μ } in a finite number of regions such that for each region there is a polynomial in μ and t that computes dim k ( Tor i S ( I t , k ) μ ) . This refines, in a graded situation, the result of Kodiyalam on Betti numbers of powers of ideals.

Our main statement treats the case of a power products of homogeneous ideals in a d -graded algebra, for a positive grading.


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Amir Bagheri. Kamran Lamei. "Graded Betti numbers of powers of ideals." J. Commut. Algebra 12 (2) 153 - 169, Summer 2020.


Received: 8 November 2016; Revised: 29 May 2017; Accepted: 9 June 2017; Published: Summer 2020
First available in Project Euclid: 2 June 2020

zbMATH: 07211332
MathSciNet: MR4105541
Digital Object Identifier: 10.1216/jca.2020.12.153

Primary: 13A30, 13D02, 13D40

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium


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Vol.12 • No. 2 • Summer 2020
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