ON FIBER CONES OF m-PRIMARY IDEALS
نویسنده
چکیده
Two formulas for the multiplicity of the fiber cone F (I) = ⊕∞n=0I /mI of an m-primary ideal of a d-dimensional Cohen-Macaulay local ring (R,m) are derived in terms of the mixed multiplicity ed−1(m|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 m-primary ideals with a d-generated minimal reduction J satisfying (i) l(I/JI) = 1 or (ii) l(Im/Jm) = 1.
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