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Cohen–Macaulay Multi–Rees Algebras

Published online by Cambridge University Press:  04 December 2007

Eero Hyry
Eero Hyry
Affiliation:
National Defence College, Santahamina, FIN–00860, Helsinki, Finland. E–mail: eero.hyry@helsinki.fi
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Abstract

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Let A be a local ring, and let I1,…,Ir ⊂ A be ideals of positive height. In this article we compare the Cohen–Macaulay property of the multi–Rees algebra RA(I1,…,Ir) to that of the usual Rees algebra RA(I1 ··· Ir) of the product I1 ··· Ir. In particular, when the analytic spread of I1 ··· Ir is small, this leads to necessary and sufficient conditions for the Cohen–Macaulayness of RA(I1,…,Ir). We apply our results to the theory of joint reductions and mixed multiplicities.

Keywords

multi–Rees algebraCohen–Macaulayjoint reductionmixed multiplicity
Type
Research Article
Information
Compositio Mathematica , Volume 130 , Issue 3 , February 2002 , pp. 319 - 343
Copyright
© 2002 Kluwer Academic Publishers