On Fiber Coefficients of Fiber Cones^†

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

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 F_K(I) ≥ d − 2, and r(I|K) < ∞, we calculate the fiber coefficients f_i(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 F_K(I) ≥ d − 2.

Key Words:

• Depth
• Fiber coefficients
• Fiber cones
• Rees-superficial sequence

2000 Mathematics Subject Classification:

• 13A15
• 13A30
• 13H15
• 13C15

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).