Abstract
Recently, Carlini, Catalisano, Guardo and Van Tuyl introduced a new construction using the Hadamard product to present star configurations of codimension c of ℙn and which they called Hadamard star configurations. We introduce a more general type of Hadamard star configuration; any star configuration constructed by our approach is called a weak Hadamard star configuration. We classify weak Hadamard star configurations, and in the case c=n, we investigate the existence of a (weak) Hadamard star configuration which is apolar to the generic homogeneous polynomials of degree d.
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