On the structure of the Hartshorne-Rao module of curves on surfaces of minimal degree

摘要

We study curves on a smooth rational scroll surface S, in particular the multiplicative structure of the Hartshorne-Rao module MC of any curve C c S. The main result is the construction of the minimal generators of M-C. As a consequence, we get that for curves C on a rational normal scroll surface, the Hilbert function of MC determines the module structure. This is a strong form of the converse of the Hartshorne-Schenzel Theorem.