J multiplicity - Alchetron, The Free Social Encyclopedia

In algebra, a j-multiplicity is a generalization of a Hilbert–Samuel multiplicity. For m-primary ideals, the two notions coincide.

Definition

Let ( R , m ) be a local Noetherian ring of Krull dimension d > 0 . Then the j-multiplicity of an ideal I is

j ( I ) = j ( gr I ⁡ R )

where j ( gr I ⁡ R ) is the normalized coefficient of the degree d − 1 term in the Hilbert polynomial Γ m ( gr I ⁡ R ) ; Γ m means the space of sections supported at m .

References

J-multiplicity Wikipedia

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