Multivariate discriminant and iterated resultant

In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f(x n ) with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant .(f) is a factor of the squarefreed iterated resultant. In fact, we find a factor Hp(f, [x 1,...,x n]) of the squarefreed iterated resultant, and prove that the multivariate discriminant .(f) is a factor of Hp(f, [x 1,...,x n]). Moreover, we conjecture that Hp(f, [x 1,...,x n]) = .(f) holds for generic form f, and show that it is true for generic trivariate form f(x, y, z).