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Search: MSC category 13A02 ( Graded rings [See also 16W50] )

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1. CJM Online first

Galetto, Federico; Geramita, Anthony Vito; Wehlau, David Louis
Degrees of regular sequences with a symmetric group action
We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.

Keywords:Complete intersection, symmetric group, regular sequences
Categories:13A02, 13A50, 20C30

2. CJM 2007 (vol 59 pp. 109)

Jayanthan, A. V.; Puthenpurakal, Tony J.; Verma, J. K.
On Fiber Cones of $\m$-Primary Ideals
Two formulas for the multiplicity of the fiber cone $F(I)=\bigoplus_{n=0}^{\infty} I^n/\m I^n$ of an $\m$-primary ideal of a $d$-dimensional Cohen--Macaulay local ring $(R,\m)$ are derived in terms of the mixed multiplicity $e_{d-1}(\m | I)$, the multiplicity $e(I)$, and superficial elements. As a consequence, the Cohen--Macaulay property of $F(I)$ when $I$ has minimal mixed multiplicity or almost minimal mixed multiplicity is characterized in terms of the reduction number of $I$ and lengths of certain ideals. We also characterize the Cohen--Macaulay and Gorenstein properties of fiber cones of $\m$-primary ideals with a $d$-generated minimal reduction $J$ satisfying $\ell(I^2/JI)=1$ or $\ell(I\m/J\m)=1.$

Keywords:fiber cones, mixed multiplicities, joint reductions, Cohen--Macaulay fiber cones, Gorenstein fiber cones, ideals having minimal and almost minimal mixed multiplicities
Categories:13H10, 13H15, 13A30, 13C15, 13A02

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