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 Delta(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 Delta(f) is a factor of Hp(f, [x(1),..., x(n)]). Moreover, we conjecture that Hp(f, [x(1),..., x(n)]) = Delta(f) holds for generic form f, and show that it is true for generic trivariate form f(x,y,z).