Applications of Koszul homology to numbers of generators and syzygies

AbstractSeveral spectral sequence techniques are used in order to derive information about the structure of finite free resolutions of graded modules. These results cover estimates of the minimal number of generators of defining ideals of projective varieties. In fact there are generalizations of a classical result of Dubreil. On the other hand there are investigations about the shifts and the dimension of Betti numbers. To this end there is a local analogue of Green's considerations developed in [5]