j-multiplicity
Appearance
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
- Katz, Daniel; Validashti, Javid (2010). "Multiplicities and Rees valuations". Collectanea Mathematica. 61: 1–24. CiteSeerX 10.1.1.509.99. doi:10.1007/BF03191222. Zbl 1216.13016. Archived from the original on 2012-06-21. Retrieved 2014-05-18.