On the resolution of certain graded algebras

Abstract

Let A = R/I be a graded algebra over the polynomial ring R = k[Xo, ... , X"\.Some properties of the numerical invariants in a minimal free resolution of A are discussed in the case A is a "Short Graded Algebra".When A is the homogeneous coordinate ring of a set of points in generic position in the projective space, several result are obtained on the line traced by some conjectures proposed by Green and Lazarsfeld in [GL] and Lorenzini in [LI]