Symmetric tensors with applications to Hilbert schemes

Roy M. Skjelnes

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arXiv · math/9912141

Symmetric tensors with applications to Hilbert schemes

Roy M. Skjelnes

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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 $\text{Symm}^n_A(A[X]_U)$ give as the ring of symmetric tensors of $\otimes_A^nA[X]_U$. The universal family is given as $\text{Symm}^{n-1}_A(A[X]_U)\times_A \text{Spec}(A[X]_U)$.

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BibTeX RIS

Roy M. Skjelnes. 1999-12-17. Symmetric tensors with applications to Hilbert schemes. https://arxiv.org/abs/math/9912141

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