= Based rational-map moduli of sigma-model lumps
{title2=$\dim_{\mathbb C}\mathcal R_k^*=2k$}
Fix the value $w(\infty)=0$ for positive-degree <sigma-model lumps>. Their holomorphic <rational maps> can be written $p/q$, where $q$ is monic of degree $k$, $p$ has degree at most $k-1$, and the polynomials have no common zero. The coefficients of $p$ and the nonleading coefficients of $q$ give $2k$ complex parameters; coprimality is an open condition. The <topological degree> is $k$, obtained by counting generic preimages with multiplicity. Allowing a common factor lowers the degree after cancellation and can describe a degeneration rather than another smooth point of this degree-$k$ parameter space.
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