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Rees algebras and mixed multiplicities


Author: J. K. Verma
Journal: Proc. Amer. Math. Soc. 104 (1988), 1036-1044
MSC: Primary 13H15; Secondary 13H10
DOI: https://doi.org/10.1090/S0002-9939-1988-0929432-4
MathSciNet review: 929432
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Abstract: Let $ (R,m)$ be a local ring of positive dimension $ d$ and $ I$ and $ J$ two $ m$-primary ideals of $ R$. Let $ T$ denote the Rees algebra $ R[Jt]$ localized at the maximal homogeneous ideal $ (m,Jt)$. It is proved that

$\displaystyle e((I,Jt)T = {e_0}(I\vert J) + {e_1}(I\vert J) + \cdots + {e_{d - 1}}(I\vert J),$

where $ {e_i}(I\vert J),i = 0,1, \ldots ,d - 1$ are the first $ d$ mixed multiplicities of $ I$ and $ J$. A formula due to Huneke and Sally concerning the multiplicity of the Rees algebra (of a complete zero-dimensional ideal of a two dimensional regular local ring) at its maximal homogeneous ideal is recovered.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0929432-4
Keywords: Bhattacharya polynomial, contracted ideal, integral closure of an ideal, joint reduction, mixed multiplicities, Rees algebra, regular local ring
Article copyright: © Copyright 1988 American Mathematical Society

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