ABSTRACT
Contents 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 Hilbert Coefficients and Associated Graded Rings . . . . . . . . . . . . . . . . . . 43 2.3 Hilbert Coefficients and Special Fiber Rings . . . . . . . . . . . . . . . . . . . . . . . 55 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.1 Introduction Our basic object of study is a Cohen-Macaulay local ring (R,m) of dimen-
sion d and its R-ideals. The examination of the asymptotic properties of such ideals has evolved into a challenging area of research, touching most aspects of commutative algebra, including its interaction with computational algebra and algebraic geometry. It takes expression in several graded algebras attached to I , among which we single out the Rees algebra R[I t], the associated graded ring grI (R) and the special fiber ring F(I ) of I ; namely,
R[I t] = ∞⊕
k=0 I k tk, grI (R) = R[I t]/IR[I t], F(I ) = R[I t]/mR[I t].
