Symmetric products and invariants of matrices
-- Francesco Vaccarino

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 Let X=Spec(R) with R a commutative ring. We will give an
explicit embedding of the n-th symmetric product of X into a
variety of tuples of matrices modulo the action of simultaneous
conjugation. Comparison with the Hilbert-Chow morphism and the
Grothendieck-Deligne-Iversen linear determinant will be
given. In the characteristic zero case we shed some light on
the variety of commuting matrices and some related topics.