Gorenstein points in $\mathbb{P}^3$ via Hadamard product of projective varieties

Abstract

We show how to construct a stick figure of lines in $\mathbb{P}^3$ using the Hadamard product of projective varieties. Then, applying the results of Migliore and Nagel, we use such stick figure to build a Gorenstein set of points with given $h-$vector ${\mathbf h}$. Since the Hadamard product is a coordinate-wise product, we show, at the end, how the coordinates of the points, in the Gorenstein set, can be directly determined.