Sally Modules and Associated Graded Rings

نویسندگان

  • Alberto Corso
  • Claudia Polini
  • Maria Vaz Pinto
  • M. Vaz Pinto
چکیده

To frame and motivate the goals pursued in the present article we recall that, loosely speaking, the most common among the blowup algebras are the Rees algebra R[It] = ⊕∞ n=0 I ntn and the associated graded ring grI(R) = ⊕∞ n=0 I n/In+1 of an ideal I in a commutative Noetherian local ring (R,m). The three main clusters around which most of the current research on blowup algebras has been developed are: (a) the study of the depth properties of R[It], or of an appropriate object related to it such as its Proj; (b) the comparison between the arithmetical properties of R[It] and grI(R); (c) the correspondence between the Hilbert/Hilbert–Samuel functions and the properties of grI(R) for an m-primary ideal I. In this paper we address the relation mentioned in (c). To make the terminology more precise, the Hilbert–Samuel function is the numerical function that measures the growth of the length of R/In, λ(R/In), for all n ≥ 1. It is well known that for n ≫ 0 this function is a polynomial in n of degree d, namely

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تاریخ انتشار 1997