LOCAL COHOMOLOGY OF REES-ALGEBRAS AND HILBERT-FUNCTIONS

Let I be an ideal primary to the maximal ideal in a local ring. We uti lize two well-known theorems due to J.-P. Serre to prove that the diff erence between the Hilbert function and the Hilbert polynomial of I is the alternating sum of the graded pieces of the graded local cohomolo gy (with respect to its positively-graded ideal) of the Pees ring Of I . This gives new insight into the higher Hilbert coefficients of I. Th e result is inspired by one due to J. D. Sally in dimension two and is implicit in a paper by D. Kirby and H. A. Mehran, where very differen t methods are used.