Nagoya Mathematical Journal

Fiber cones of ideals with almost minimal multiplicity

A. V. Jayanthan and J. K. Verma

Full-text: Open access

Abstract

Fiber cones of $0$-dimensional ideals with almost minimal multiplicity in Cohen-Macaulay local rings are studied. Ratliff-Rush closure of filtration of ideals with respect to another ideal is introduced. This is used to find a bound on the reduction number with respect to an ideal. Rossi's bound on reduction number in terms of Hilbert coefficients is obtained as a consequence. Sufficient conditions are provided for the fiber cone of $0$-dimensional ideals to have almost maximal depth. Hilbert series of such fiber cones are also computed.

Article information

Source
Nagoya Math. J., Volume 177 (2005), 155-179.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114632161

Mathematical Reviews number (MathSciNet)
MR2124550

Zentralblatt MATH identifier
1075.13011

Subjects
Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13H15: Multiplicity theory and related topics [See also 14C17]
Secondary: 13C15, 13A02: Graded rings [See also 16W50]

Citation

Jayanthan, A. V.; Verma, J. K. Fiber cones of ideals with almost minimal multiplicity. Nagoya Math. J. 177 (2005), 155--179. https://projecteuclid.org/euclid.nmj/1114632161


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