Table of Contents
Algebra
Volume 2014 (2014), Article ID 970157, 7 pages
http://dx.doi.org/10.1155/2014/970157
Research Article

On Determinantal Varieties of Hankel Matrices

1University of Trento, 38123 Povo, Trento, Italy
2Polytechnic of Turin, 10129 Torino, Italy

Received 23 January 2014; Accepted 9 April 2014; Published 28 April 2014

Academic Editor: Sorin Dascalescu

Copyright © 2014 Edoardo Ballico and Michele Elia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a class of Hankel matrices whose entries, depending on a given matrix , are linear forms in variables with coefficients in a finite field . For every matrix in , it is shown that the varieties specified by the leading minors of orders from 1 to have the same number of points in . 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.