J-multiplicity

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

Definition

Let be a local Noetherian ring of Krull dimension . Then the j-multiplicity of an ideal I is

where is the normalized coefficient of the degree d − 1 term in the Hilbert polynomial ; means the space of sections supported at .

References

• Daniel Katz, Javid Validashti, Multiplicities and Rees valuations