Stratification and coordinate systems for the moduli space of rational functions

Fujimura, Masayo; Taniguchi, Masahiko

doi:10.1090/S1088-4173-10-00207-9

Stratification and coordinate systems for the moduli space of rational functions
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by Masayo Fujimura and Masahiko Taniguchi

Conform. Geom. Dyn. 14 (2010), 141-153

DOI: https://doi.org/10.1090/S1088-4173-10-00207-9

Published electronically: May 5, 2010

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Abstract:

In this note, we give a new simple system of global parameters on the moduli space of rational functions, and clarify the relation to the parameters indicating location of fixed points and the indices at them. As a byproduct, we solve a conjecture of Milnor affirmatively.

References

D. Cox, J. Little, and D. O’Shea, Ideals, varieties, and algorithms, UTM, Springer-Verlag, 1998.
David Cox, John Little, and Donal O’Shea, Using algebraic geometry, Graduate Texts in Mathematics, vol. 185, Springer-Verlag, New York, 1998. MR 1639811, DOI 10.1007/978-1-4757-6911-1
Masayo Fujimura, The moduli space of rational maps and surjectivity of multiplier representation, Comput. Methods Funct. Theory 7 (2007), no. 2, 345–360. MR 2376676, DOI 10.1007/BF03321649
Masayo Fujimura and Masahiko Taniguchi, A compactification of the moduli space of polynomials, Proc. Amer. Math. Soc. 136 (2008), no. 10, 3601–3609. MR 2415044, DOI 10.1090/S0002-9939-08-09344-1
Curt McMullen, Families of rational maps and iterative root-finding algorithms, Ann. of Math. (2) 125 (1987), no. 3, 467–493. MR 890160, DOI 10.2307/1971408
John Milnor, Geometry and dynamics of quadratic rational maps, Experiment. Math. 2 (1993), no. 1, 37–83. With an appendix by the author and Lei Tan. MR 1246482, DOI 10.1080/10586458.1993.10504267
John Milnor, Dynamics in one complex variable, 3rd ed., Annals of Mathematics Studies, vol. 160, Princeton University Press, Princeton, NJ, 2006. MR 2193309