Betti numbers of perfect homogeneous ideals

In this paper we study the graded minimal free resolution of the ideal, I, of any arithmetically Cohen-Macaulay projective variety. First we determine the range of the shifts (twisting numbers) that can possibly occur in the resolution, in terms of the Hilbert function of I. Then we find conditions under which some of the twisting numbers do not occur. Finally, in some ‘good’ cases, all the Betti numbers are (recursively) computed, in terms of the Hilbert function of I or that of Extⁿ_R(R/I,R), where R is a polynomial ring over a field and n is the height of I in R.