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On the Cohen-Macaulayness of fiber cones

Author(s): Duong Quôc Vi\d êt
Journal: Proc. Amer. Math. Soc. 136 (2008), 4185-4195.
MSC (2000): Primary 13H10; Secondary 13A15, 13A30, 13C14, 13H15
Posted: July 23, 2008
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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 Vi\d êt
Affiliation: Department of Mathematics, Hanoi University of Education, Xuan Thuy Street, Hanoi, Vietnam
Email: duongquocviet@fmail.vnn.vn

DOI: 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
Posted: July 23, 2008
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2008, American Mathematical Society

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