Collectanea mathematica

, Volume 61, Issue 1, pp 1-24

First online:

Multiplicities and Rees valuations

  • Daniel KatzAffiliated withDepartment of Mathematics, University of Kansas Email author 
  • , Javid ValidashtiAffiliated withDepartment of Mathematics, University of Kansas

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Let (R;m) be a local ring of Krull dimensiond andIR 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.


Rees valuation jmultiplicity quasiunmixed local ring


Primary 13H15 13A30 Secondary 13J10