On Hilbert Functions of Points in Projective Space and Structure of Graded Modules

Abstract

In this paper, we investigate the relationship between the Hilbert functions and the associated properties of the graded modules. To attain this, we construct the graded modules from the sets of points in projective space, $\mathbb{P}_k^n$ . We use a computer software package for algebraic computations Macaulay2 to study the Hilbert functions and the associated properties of the graded modules. Thereafter, we provide theoretical proofs of the results obtained from Macaulay2 and finally, we give illustrative examples to justify some of our results.