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Properties of the Fiber Cone of Ideals in Local Rings
Abstract:Abstract

For an ideal I of a Noetherian local ring (R, m ) we consider properties of I and its powers as reflected in the fiber cone F(I) of I. In particular,we examine behavior of the fiber cone under homomorphic image R → R/J = R′ as related to analytic spread and generators for the kernel of the induced map on fiber cones ψ J  : F R (I) → F R(IR′). We consider the structure of fiber cones F(I) for which ker ψ J  ≠ 0 for each nonzero ideal J of R. If dim F(I) = d > 0,μ(I) = d + 1 and there exists a minimal reduction J of I generated by a regular sequence,we prove that if grade(G +(I)) ≥ d ? 1,then F(I) is Cohen-Macaulay and thus a hypersurface.
Keywords:Fiber cone  Analytic spread  Multiplicity  Cohen-Macaulay ring
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