Bounds for Betti numbers and the degrees of the generators of syzygies in graded resolutions (Q6637179)

The paper aims to size up the minimal graded free resolution of a homogeneous ideal in terms of its generating degree. The main tools used in the paper are spectral sequences and the Boij-Söderberg theory of Betti diagrams. Section 2 is devoted to subadditivity estimates for the degrees of a resolution. There are several applications of this, for instance estimates for the Green-Lazarsfeld invariant. Moreover when \(S\) is a standard graded polynomial ring the paper deals with a more direct estimate of the degrees and Betti numbers of the minimal free \(S\)-resolution of \(R=S/I\), where \(I\) is homogeneous and \(d\)-equigenerated. One main tool here is the Boij-Söderberg theory of Betti diagrams. Section 4 deals with the case where \(I\) is the Jacobian ideal \(J_f\) of a form \(f\). Upper bounds for the regularity of \(J^{sat}_f/J_f\).