Let $X$ be smooth projective curve of genus $g$. Let $R(g,n)$ be $Hom(\pi_1(X),GL_n(C)$ with the natural affine scheme structure. If $g>1$, it is known that the representation space $R(g,n)$ is an irreducible reduced normal complete intersection. When $g=1$, it is conjectured that it is reduced and normal. In small values of $g$ and $n$, can you find the singularities of $R(g,n)$? If so, can you resolve them? Does $R(g,n)$ have rational or klt singularities?

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