Buchsbaumness of the associated graded rings of filtration

2020/03/23 by Saloni, Kumari
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.10156

Abstract

Let (A,\mathfrakm) be a Noetherian local ring of dimension d>0 and I an I-primary ideal of A. In this paper, we discuss a sufficient condition, for the Buchsbaumness of the local ring A to be passed onto the associated graded ring of filtration. Let I denote an I-good filtration. We prove that if A is Buchsbaum and the I-invariant, I(A) and I(G(I)), coincide then the associated graded ring G(I) is Buchsbaum. As an application of our result, we indicate an alternative proof of a conjecture, of Corso on certain boundary conditions for Hilbert coefficients.

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