2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79626Let A[X]_U be a fraction ring of the polynomial ring A[X] in the variable X over a commutative ring A. We show that the Hilbert functor {Hilb}^n_{A[X]_U} is represented by an affine scheme $\text{Symm}^n_A(A[X]_U)$ give as the ring of symmetric tensors of $\otimes_A^nA[X]_U$. The universal family is given as $\text{Symm}^{n-1}_A(A[X]_U)\times_A \text{Spec}(A[X]_U)$.Algebraic Geometrytext