ABSTRACT
Let R be a local ring of dimension d 0 and I an -primary ideal of R. The blowup algebras RIt
n0 Intn and grIR RItIRIt are key ingredients in the process of resolving singularities. The numerical functions that gauge the complexity of the above graded rings are fundamental tools. The function HI;n grIRn is called the Hilbert function of I; as known, it is a polynomial in n for all n 0. The iterated Hilbert function H1I;n ∑ni0 HI; i is also a polynomial in n for all n 0, denoted by h1I;n. This can be written in the form ∑dq01qeqI
. The eqI are the Hilbert coefficients of the ideal I.
