Let $V$ be finite dimensional vector space over the field of complex numbers. Let $G$ be a finite subgroup of $GL(V)$, group of all $\mathbb{C}$- linear automorphisms of $V$. Then, the apmple generator of the Picard group of the projective space $\mathbb P(V)$ descends to the quotient variety $\mathbb{P}(V)/G$. Let $L$ denote the descent. We prove that the polarised variety $\mathbb P(V)/G, L$ is projectively normal when $G$ is solvable or $G$ is generated by pseudo reflections.

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Last updated: 23 Jun 2024