Existence and formulas regarding the epsilon multiplicity
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The volume of an mR-primary graded family of ideals is the natural generalization of the Hilbert-Samuel multiplicity to arbitrary mR-primary graded families. Lazarsfeld and Mustata, and more generally, Cutkosky, have developed a formula (called volume equals multiplicity) for showing that the volume of a graded family is a limit of Hilbert-Samuel multiplicities. We show that the analogue of this fact for non mRprimary graded families holds in the case that the graded family arises from an ideal. We accomplish this by first proving a more general multiplicity formula.
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PhD