On fiber cones of m-primary ideals
A. V. Jayanthan, Tony J. Puthenpurakal, J. K. Verma
Abstract
Two formulas for the multiplicity of the fiber cone F(I)=n=0∞ In/ In of an -primary ideal of a d-dimensional Cohen-Macaulay local ring (R,) are derived in terms of the mixed multiplicity ed-1( | I), the multiplicity e(I) and superficial elements. As a consequence, the Cohen-Macaulay property of F(I) when I has minimal mixed multiplicity or almost minimal mixed multiplicity is characterized in terms of reduction number of I and lengths of certain ideals. We also characterize Cohen-Macaulay and Gorenstein property of fiber cones of -primary ideals with a d-generated minimal reduction J satisfying (i) (I2/JI)=1 or (ii) (I/J)=1.
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