Gorenstein points in {mathbb {P}}^{3} via Hadamard products 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 a stick figure to build a Gorenstein set of points with given h-vector {varvec{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.