Geodesic
The moduli space of quadratic rational maps
DeMarco, Laura1
1Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Journal of the American Mathematical Society, Tome 20 (2007) no. 2, pp. 321-355

Voir la notice de l'article provenant de la source American Mathematical Society

Let $M_2$ be the space of quadratic rational maps $f:\textbf {P}^1\to \textbf {P}^1$, modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification $X$ of $M_2$ is defined, as a modification of Milnor’s $\overline {M}_2\simeq \textbf {CP}^2$, by choosing representatives of a conjugacy class $[f]\in M_2$ such that the measure of maximal entropy of $f$ has conformal barycenter at the origin in $\textbf {R}^3$ and taking the closure in the space of probability measures. It is shown that $X$ is the smallest compactification of $M_2$ such that all iterate maps $[f]\mapsto [f^n]\in M_{2^n}$ extend continuously to $X \to \overline {M}_{2^n}$, where $\overline {M}_d$ is the natural compactification of $M_d$ coming from geometric invariant theory.
DOI : 10.1090/S0894-0347-06-00527-3

DeMarco, Laura  1

1 Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637 
DeMarco, Laura. The moduli space of quadratic rational maps. Journal of the American Mathematical Society, Tome 20 (2007) no. 2, pp. 321-355. doi: 10.1090/S0894-0347-06-00527-3
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