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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The moduli space of quadratic rational maps
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by Laura DeMarco PDF
J. Amer. Math. Soc. 20 (2007), 321-355 Request permission

Abstract:

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.
References
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Additional Information
  • Laura DeMarco
  • Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
  • MR Author ID: 677013
  • Email: demarco@math.uchicago.edu
  • Received by editor(s): February 28, 2005
  • Published electronically: February 16, 2006
  • Additional Notes: Research was partially supported by an NSF Postdoctoral Fellowship
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 20 (2007), 321-355
  • MSC (2000): Primary 37F45; Secondary 14L24, 57M50
  • DOI: https://doi.org/10.1090/S0894-0347-06-00527-3
  • MathSciNet review: 2276773