# Complements to duals of smooth curves

Suppose that $C\subset \mathbb P^2$ is a smooth curve (over $\mathbb C$) and $C^*\subset (\mathbb P^2)^*$ is its dual curve. What is known about $\pi_1$ of the complement to $C^*$ in $(\mathbb P^2)^*$? I am particularly interested in smooth curves of low degree.

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In the particular case where $C^*$ is a degree 6 curve with 9 ordinary cusps, i.e., the dual of a smooth cubic, th Alexander polynomial equals $(t^2-t+1)^3$, which implies that the fundamental group is highly non-abelian.