Rational normal curves and Hadamard products

Given r > n general hyperplanes in Pn , a star configuration of points is the set of all the n-wise intersection of the hyperplanes. We introduce contact star configurations, which are star configurations where all the hyperplanes are osculating to the same rational normal curve. In this paper, we find a relation between this construction and Hadamard products of linear varieties. Moreover, we study the union of contact star configurations on a same conic in P2 , we prove that the union of two contact star configurations has a special h-vector and, in some cases, this is a complete intersection.