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Original Articles

On Fiber Coefficients of Fiber ConesFootnote

Pages 4120-4131 | Received 15 Jun 2007, Published online: 02 Dec 2008
 

Abstract

Let (R,𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When depth G(I) ≥ d − 1, depth FK(I) ≥ d − 2, and r(I|K) < ∞, we calculate the fiber coefficients fi(I). Under the above assumptions on depth G(I) and r(I|K), we give an upper bound for f1(I), and also provide a characterization, in terms of f1(I), of the condition depth FK(I) ≥ d − 2.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENT

I would like to thank Professor Zhong-Ming Tang for useful discussions, and the referee for a careful reading and pertinent comments.

Notes

Communicated by I. Swanson.

Supported by the National Natural Science Foundation of China (10771152).

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