For each Montesinos knot $K$, we propose an efficient method to explicitly determine the irreducible ${ \rm SL}(2,\mathbb{ C})$-character variety, and show that it can be decomposed as $\mathcal{ X}_0(K)\sqcup\mathcal{ X}_1(K)\sqcup\mathcal{ X}_2(K)\sqcup\mathcal{ X}'(K)$, where $\mathcal{ X}_0(K)$ consists of trace-free characters, $\mathcal{ X}_1(K)$ consists of characters of "unions" of representations of rational knots (or rational link, which appears at most once), $\mathcal{ X}_2(K)$ is an algebraic curve, and $\mathcal{ X}'(K)$ consists of finitely many points when $K$ satisfies a generic condition.
Categories: math.GT
