We find characterization for the distinguished varieties in symmetrized polydisc $\mathbb G_n \; (n\geq 2)$ and thus generalize work [\textit{J. Funct. Anal.}, 266 (2014), 5779 -- 5800] on G_2$ by author Shalit. show that a variety $\Lambda$ G_n$ is part of an algebraic curve, which set-theoretic complete intersection, can be represented Taylor joint spectrum $n-1$ commuting scalar matrices sat...