On the Cohen-Macaulayness of fiber cones
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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.References
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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
- 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
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 4185-4195
- MSC (2000): Primary 13H10; Secondary 13A15, 13A30, 13C14, 13H15
- DOI: https://doi.org/10.1090/S0002-9939-08-09438-0
- MathSciNet review: 2431031