Difference Chow form

In this paper, the generic intersection theory for difference varieties is presented. Precisely, the intersection of an irreducible difference variety of dimension d>0d>0 and order h with a generic difference hypersurface of order s   is shown to be an irreducible difference variety of dimension d−1d−1 and order h+sh+s. Based on the intersection theory, the difference Chow form for an irreducible difference variety is defined. Furthermore, it is shown that the difference Chow form of an irreducible difference variety V is transformally homogeneous and has the same order as V.