摘要
In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant A（f） is a factor of the squarefreed iterated resulrant. In fact, we find a factor Hp（f, [x1 , xn]） of the squarefreed iterated resultant, and prove that the multivariate discriminant A（f） is a factor of Hp（f,[x1,... ,xn]）. Moreover, we conjecture that Hp（f, [x1,..., xn]） =△（f） holds for generic form f, and show that it is true for generic trivariate form f（x, y, z）.
In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant A（f） is a factor of the squarefreed iterated resulrant. In fact, we find a factor Hp（f, [x1 , xn]） of the squarefreed iterated resultant, and prove that the multivariate discriminant A（f） is a factor of Hp（f,[x1,... ,xn]）. Moreover, we conjecture that Hp（f, [x1,..., xn]） =△（f） holds for generic form f, and show that it is true for generic trivariate form f（x, y, z）.
基金
Supported by China Scholarship Council
