Recently, Carlini, Catalisano, Guardo and Van Tuyl introduced a new construction using the Hadamard product to present star configurations of codimension of 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 , we investigate the existence of a (weak) Hadamard star configuration which is apolar to the generic homogeneous polynomials of degree .
"Weak Hadamard star configurations and apolarity." Rocky Mountain J. Math. 50 (3) 851 - 862, June 2020. https://doi.org/10.1216/rmj.2020.50.851