FIBER CONES WITH ALMOST MAXIMAL DEPTH

ABSTRACT

Let A be a noetherian local ring with dimension d and I be an ideal of A . Let E=( E _n )n≥ 0 be a good I-filtration of submodules of an A-module E . Let H be an ideal of A containing I and F _H E) = ⨁n ≥  0 E _n / HE n . Assume that E is a Cohen–Macaulay module with λ(E/IE) finite and Ann(E) = 0, and let J be a minimal reduction of I. In this paper we give conditions on λ(E _n  ∩ JE/JE _n−1) and λ(HE _n  ∩ JE/JHE _n−1) so, that F _H (E), has depth of at least d − 1.

Key Words:

• Cohen–Macaulay module
• Depth
• Fiber cones

1991 Mathematics Subject Classification:

• Primary 13C15
• Secondary 13C14

ACKNOWLEDGMENT

The author would like to thank Santiago Zarzuela for valuable conversations and suggestions.

Notes

^#Communicated by A. Facchini.