2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225943We prove that for an abelian group $G$ of order $n$ the morphism $ φ\colon \mathbf{P}(V^*)\longrightarrow \mathbf{P} ((\mathrm{sym}^n V^*)^G)$ defined by $φ([f]) = [\prod_{σ\in G} σ\cdot f ]$ is nondegenerate for every finite-dimensional representation $V$ of $G$ if and only if either $n$ is a prime number or $n=4$.8 pagesAlgebraic Geometry14L30text