= Rational covering maps of the projective line
{title2=$\dim_{\mathbb C}\operatorname{Rat}_m=2m+1$}
A degree-$m$ <rational map> of the <complex projective line> is represented by two degree-at-most-$m$ polynomials without a common root, modulo common scalar multiplication. This is an open set of $\mathbb{CP}^{2m+1}$. Quotienting by domain <Möbius transformations> subtracts three complex dimensions, giving real dimension $4m-4$ for degree $m\geq2$. These are the local covering parameters of a multiple-covered <J-holomorphic sphere>.
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