LINEAR RECURRENCES AND VANDERMONDE VARIETIES. I.

Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties which we call Vandermonde varieties. They are closely related to the varieties of linear recurrence relations of a given order possessing a non-trivial solution vanishing at a given set of integers. In the regular case, i.e. when the dimension of a Vandermonde variety is the expected one we present its free resolution, obtain its degree and the Hilbert series. Many open problems and conjectures are posed.