# Algebraic stability of meromorphic maps descended from Thurston's pullback maps

@article{Ramadas2019AlgebraicSO,
title={Algebraic stability of meromorphic maps descended from Thurston's pullback maps},
journal={arXiv: Algebraic Geometry},
year={2019}
}
Let $\phi:S^2 \to S^2$ be a post-critically finite branched overing. Under certain conditions, by work of Koch, $\phi$ induces a meromorphic self-map $R_{\phi}$ on the moduli space $\mathcal{M}_{0,n}$; $R_{\phi}$ descends from Thurston's pullback map on Teichm\"uller space. Here, we relate the dynamics of $R_{\phi}$ on $\mathcal{M}_{0,n}$ to the dynamics of $\phi$ on $S^2$. We show, roughly speaking, that if $\phi$ "resembles" a topological polynomial, then $R_{\phi}$ is algebraically stable on… Expand
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