Let (R;m) be a local ring of Krull dimensiond andI ⊆R be an ideal with analytic spreadd. We show that thej-multiplicity ofI is determined by the Rees valuations ofI centered on m. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at anO(n d) rate.
KeywordsRees valuation jmultiplicity quasiunmixed local ring
MSC2000Primary 13H15 13A30 Secondary 13J10
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