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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Cohen-Macaulayness of fiber cones


Author: Duong Quôc Việt
Journal: Proc. Amer. Math. Soc. 136 (2008), 4185-4195
MSC (2000): Primary 13H10; Secondary 13A15, 13A30, 13C14, 13H15
Published electronically: July 23, 2008
MathSciNet review: 2431031
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Abstract: Let $ A$ be a Noetherian local ring with the maximal ideal $ {\mathfrak{m}}$ and $ I$ an ideal of $ A.$ Denote by $ F_{A}(I) = \underset {{n\ge 0} }{\bigoplus }(I^{n}/{\mathfrak{m}}I^{n})$ the fiber cone of $ I.$ This paper characterizes the multiplicity and the Cohen-Macaulayness of fiber cones in terms of minimal reductions of ideals.


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Additional Information

Duong Quôc Việt
Affiliation: Department of Mathematics, Hanoi University of Education, Xuan Thuy Street, Hanoi, Vietnam
Email: duongquocviet@fmail.vnn.vn

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09438-0
PII: S 0002-9939(08)09438-0
Keywords: Cohen-Macaulay ring, multiplicity, fiber cone
Received by editor(s): May 15, 2006
Received by editor(s) in revised form: November 3, 2007, and November 13, 2007
Published electronically: July 23, 2008
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society