On the Cohen-Macaulayness of fiber cones

Việt, Duong

doi:10.1090/S0002-9939-08-09438-0

On the Cohen-Macaulayness of fiber cones
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Proc. Amer. Math. Soc. 136 (2008), 4185-4195 Request permission

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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