HIGHLIGHTS
SUMMARY
The authors note that the latter condition is similar to others that have been considered in previous works regarding limits of graded families of ideals (see, e_g, Theorem 6.1). Since Vold./ D c d=d Š and MVd.;:::; / D d Š Vold./, the inequality cd MVd../.d1;:::;dr / / D MVd.;:::; / MVd../.d1;:::;dr / / follows from the monotonicity of mixed volumes (see, e_g, equation 5.25). Notice that .1;0 / . result follows from the monotonicity of mixed volumes (see, e_g, equation 5.25). This can be seen as an extension of the usual "volume=multiplicity formula . . .
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