Multiplicities and Rees valuations

• Autores: Daniel J. Katz, Javid Validashti
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 61, Fasc. 1, 2010, págs. 1-24
• Idioma: inglés
• DOI: 10.1007/bf03191222
• Enlaces
  • Texto completo
• Resumen

  • Let $(R,\m)$ be a local ring of Krull dimension~$d$ and $I\subseteq R$ be an ideal with analytic spread~$d$. We show that the $j$-multiplicity of~$I$ is determined by the Rees valuations of~$I$ centered on~$\m$. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at an~$O(n^d)$ rate.

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