Abstract
Let $(A,\frak{m})$ denote a Noetherian local ring with maximal ideal $\frak{m}$, $J$ an $\frak m$-primary ideal, $I_1,\ldots, I_s$ ideals of $A$; $M$ a finitely generated $A$-module. This paper will answer when mixed multiplicities of the multi-graded fiber cone $$ F_M(J,I_1,\ldots, I_s)=\bigoplus_{n_1,\ldots,n_s\geqslant 0}\dfrac{I_1^{n_1}\cdots I_s^{n_s}M}{JI_1^{n_1}\cdots I_s^{n_s}M} $$ are positive and characterize them in terms of the length of modules.
Citation
Quoc Viet Duong. Tien Manh Nguyen. "On the Mixed Multiplicities of Multi-graded Fiber Cones." Tokyo J. Math. 31 (2) 399 - 414, December 2008. https://doi.org/10.3836/tjm/1233844060
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