Nondegeneracy for Quotient Varieties under Finite Group Actions

Details Nondegeneracy for Quotient Varieties under Finite Group Actions Nondegeneracy for Quotient Varieties under Finite Group Actions

2009-04-06

arxiv.org/abs/0904.0853v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

We prove that for an abelian group $G$ of order $n$ the morphism $
\varphi\colon \mathbf{P}(V^*)\longrightarrow \mathbf{P} ((\mathrm{sym}^n
V^*)^G)$ defined by $\varphi([f]) = [\prod_{\sigma\in G} \sigma \cdot f ]$ is
nondegenerate for every finite-dimensional representation $V$ of $G$ if and
only if either $n$ is a prime number or $n=4$.

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