Let $S$ be a finitely generated standard multigraded algebra over an Artinian local ring $A$; $M$ a finitely generated multigraded $S$-module. This paper first investigates the relationship between the multiplicity and mixed multiplicities of $M$. Next, we give some applications to multigraded fiber cones.
"On the Multiplicity of Multigraded Modules Over Artinian Local Rings." Tokyo J. Math. 33 (2) 341 - 360, December 2010. https://doi.org/10.3836/tjm/1296483474