ON THE CANONICAL MODULE OF A 0-DIMENSIONAL SCHEME

The main topic of this paper is to give characterizations of geometric properties of 0-dimensional subschemes X subset-or-equal-to P(d) in terms of the algebraic structure of the canonical module of their projective coordinate ring. We characterize Cayley-Bacharach, (higher order) uniform position, linearly and higher order general position properties, and derive inequalities for the Hilbert functions of such schemes. Finally we relate the structure of the canonical module to properties of the minimal free resolution of X.