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Bull. Korean Math. Soc. 2020; 57(5): 1231-1240

Online first article September 7, 2020      Printed September 30, 2020

https://doi.org/10.4134/BKMS.b190906

Copyright © The Korean Mathematical Society.

Graded Betti numbers of good filtrations

Kamran Lamei, Siamak Yassemi

University of Tehran; University of Tehran

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The asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi-polynomial behavior of graded Betti numbers of powers of homogenous ideals to $\ZZ$-graded algebra over Noetherian local ring. Furthermore our main result treats the Betti table of filtrations which is finite or integral over the Rees algebra.

Keywords: Betti numbers, good filtrations, vector partition function

MSC numbers: 13A30, 13D02, 13D40, 13B22

Supported by: The rst author also acknowledge the support of Iran's National Elites Foundation(INEF)

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