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Multiplicities and Reduction Numbers

Published online by Cambridge University Press:  04 December 2007

Wolmer V. Vasconcelos
Wolmer V. Vasconcelos
Affiliation:
Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, U.S.A. e-mail: vasconce@math.rutgers.edu
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Abstract

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Let (R, ${\frak {m}}$) be a Cohen–Macaulay local ring and let I be an ideal. There are at least five algebras built on I whose multiplicity data affect the reduction number r(I) of the ideal. We introduce techniques from the Rees algebra theory of modules to produce estimates for r(I), for classes of ideals of dimension one and two. Previous cases of such estimates were derived for ideals of dimension zero.

Keywords

Cohen–Macaulay ringconormal moduleHilbert functionmultiplicityreduction numberRees algebra
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 3 , December 2003 , pp. 361 - 379
Copyright
© 2003 Kluwer Academic Publishers