Abstract
Let $A = R/I$ be a graded algebra over the polynomial ring $R = k[{X_0}, \ldots ,{X_n}]$. 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 [L1]
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