Mathematics – Algebraic Geometry
Scientific paper
2006-08-26
Mathematics
Algebraic Geometry
10 pages, from the talk given at ICM 2006 Madrid
Scientific paper
We show that the $n-$th symmetric product of an affine scheme $X=\mathrm{Spec} A$ over a characteristic zero field is isomorphic as a scheme to the quotient by the general linear group of the scheme parameterizing $n-$dimensional linear representations of $A$. As a consequence we give generators and relations of the related rings of invariants as well as the equations of any symmetric products in term of traces. In positive characteristic we prove an analogous result for the associated varieties.
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