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Joint reductions and Rees algebras

Published online by Cambridge University Press:  24 October 2008

J. K. Verma
J. K. Verma
Affiliation:
Department of Mathematics, Indian Institute of Technology, Powai, Bombay 400 076, India
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Let R be a Cohen-Macaulay local ring of dimension d, multiplicity e and embedding dimension v. Abhyankar [1] showed that v − d + 1 ≤ e. When equality holds, R is said to have minimal multiplicity. The purpose of this paper is to study the preservation of this property under the formation of Rees algebras of several ideals in a 2-dimensional Cohen-Macaulay (CM for short) local ring. Our main tool is the theory of joint reductions and mixed multiplicities developed by Rees [9] and Teissier[12].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 2 , March 1991 , pp. 335 - 342
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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