= Solution
Write the <projective plane> as $\mathbb P(V)$ for a three-dimensional complex vector space $V$. A projective line is the zero set of a nonzero linear functional $\ell\in V^*$. Two such functionals give the same line exactly when they differ by a nonzero scalar. Hence the parameter space of lines is the <dual projective space> $\mathbb P(V^*)$. A choice of basis identifies $V^*$ with $\mathbb C^3$, giving \b[$\boxed{(\mathbb P^2)^\vee\cong\mathbb P^2}$.] The description as $\mathbb P(V^*)$ is intrinsic; the identification with the original $\mathbb P(V)$ requires a choice.
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