Hilbert coefficients and the associated graded rings

Wang, Hsin-Ju

doi:10.1090/S0002-9939-99-05080-7

Hilbert coefficients
and the associated graded rings

Author: Hsin-Ju Wang
Journal: Proc. Amer. Math. Soc. 128 (2000), 963-973
MSC (1991): Primary 13A30, 13D40, 13H10
DOI: https://doi.org/10.1090/S0002-9939-99-05080-7
Published electronically: July 28, 1999
MathSciNet review: 1628432
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Abstract: Let $(R, \mathfrak{m})$ be a -dimensional Cohen-Macaulay local ring with infinite residue field. Let be an $\mathfrak{m}$ -primary ideal of . In this paper, we prove that if $\displaystyle \sum _{n=1}^{\infty} \lambda(I^n/I^{n-1}J)-e_1(I)=1$ for some minimal reduction of , then depth $G(I)\geq d-2$ .

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