Symmetric tensors with applications to Hilbert schemes

Roy M. Skjelnes

paper

Symmetric tensors with applications to Hilbert schemes

arXiv:math/9912141

Abstract

Let 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 $Symm_{A}^{n} (A [X]_{U})$ give as the ring of symmetric tensors of $\otimes_{A}^{n} A [X]_{U}$ . The universal family is given as $Symm_{A}^{n - 1} (A [X]_{U}) \times_{A} Spec (A [X]_{U})$ .