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 q n . 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 intersections.