Symmetric product as moduli space of linear representations

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dc.creatorVaccarino, F.
dc.date2006-08-26
dc.date.accessioned2026-07-07T07:22:12Z
dc.date.available2026-07-07T07:22:12Z
dc.descriptionWe 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.
dc.description10 pages, from the talk given at ICM 2006 Madrid
dc.identifierhttps://arxiv.org/abs/math/0608655
dc.identifierhttp://arxiv.org/abs/math/0608655
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115571
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14L30, 13A50, 20G05
dc.titleSymmetric product as moduli space of linear representations
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