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We discuss the theory of multiplicities and mixed multiplicities of filtrations of m-primary ideals. We show that many classical formulas are true in this setting. We also consider the case of equality in Minkowski's inequality. We give some general theorems characterizing when this condition holds, giving generalizations of classical theorems of Rees, Sharp, Teissier, Katz and others.Updated on Jun 15, 2020 11:18 AM PDT
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