Betti numbers of perfect homogeneous ideals (Q914759)

The paper deals with the graded minimal free resolutions of perfect homogeneous ideals I in a polynomial ring R over a field k. First the author determines the numbers and the range of the twisting numbers of I by showing that the degrees in which \(Tor_ i^ R(I,k)\) is not vanishing are related to the degrees in which generators of I are occuring (see theorem 2.2). There are interesting applications of theorem 2.2 in this section 2. Then conditions are given where some of the twisting numbers will not appear (see theorem 3.2). Finally theorem 3.2 is specialized to particular situations in which the Betti numbers of I can be computed section 4).