Hadamard Star Configurations

Bocci, Carlini and Kileel have shown that the square-free Hadamard product of a finite set of points Z that all lie on a line ℓ in Pn produces a star configuration of codimension n. In this paper, we introduce a construction using the Hadamard product to construct star configurations of codimension c. In the case that c=n=2, our construction produces the star configurations of Bocci, Carlini and Kileel. We will call any star configuration that can be constructed using our approach a Hadamard star configuration. Our main result is a classification of Hadamard star configurations.