Resultants and symmetric products

We use the symmetric product Sym(n) ( P-k(1) ) of the projective line to describe the resultant scheme R-n,R-m in P-k(n) x P-k(m) as a quotient X/G where X=(P-k(1))(n+m) and G subset of Aut(k) (X) is a finite subgroup. As a special case we give a description of the discriminant scheme in terms of the symmetric product.We use the symmetric product of the projective line to describe the resultant scheme R n , m in as a quotient X / G where and G subset of Aut k ( X ) is a finite subgroup. As a special case we give a description of the discriminant scheme in terms of the symmetric product.