Invariant Algebraic Sets and Symmetrization of Polynomial Systems
Résumé
Assuming the variety of a polynomial set is invariant under a group action, we construct a set of invariants that define the same variety. Our construction can be seen as a generalization of the previously known construction for finite groups once we introduce the symmetrizations of a polynomial w.r.t. a section to the orbits of the group action. The symmetrisations are polynomials in a generating set of rational invariants as constructed in [9]. The results have thus to be understood outside of a proper closed invariant variety, independent of the polynomial set considered.
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