On curves with natural cohomology and their deficiency modules
We give necessary numerical conditions on the minimal free resolution of the Hartshorne-Rao module of a curve with natural cohomology. We show with an example that the multiplication between two consecutive homogeneous components of the module need not to be of maximal rank. We apply these ideas in order to get smoothness and unicity results (in the case of a module of diameter 2 or 3) for the components of the Hilbert schemes containing curves with natural cohomology.
scientific article; zbMATH DE number 425533
scientific article