On fiber cones of -primary ideals
arXiv:math/0408346
Abstract
Two formulas for the multiplicity of the fiber cone $F(I)=\oplus_{n=0}^{\infty} I^n/\m I^n$ of an $\m$-primary ideal of a -dimensional Cohen-Macaulay local ring $(R,\m)$ are derived in terms of the mixed multiplicity $e_{d-1}(\m | I),$ the multiplicity and superficial elements. As a consequence, the Cohen-Macaulay property of when has minimal mixed multiplicity or almost minimal mixed multiplicity is characterized in terms of reduction number of and lengths of certain ideals. We also characterize Cohen-Macaulay and Gorenstein property of fiber cones of $\m$-primary ideals with a -generated minimal reduction satisfying (i) or (ii) $\ell(I\m/J\m)=1.$
17 Pages