On Determinantal Varieties of Hankel Matrices

Let H be a class of n × n Hankel matrices H_A whose entries, depending on a given matrix A, are linear forms in n variables with coefficients in a finite field F_q. For every matrix in H, it is shown that the varieties specified by the leading minors of orders from 1 to n − 1 have the same number q^(n−1) of points in F^n_q . Further properties are derived, which show that sets of varieties, tied to a given Hankel matrix, resemble a set of hyperplanes as regards the number of points of their intersection