A compactification of the moduli space of polynomials
HTML articles powered by AMS MathViewer
- by Masayo Fujimura and Masahiko Taniguchi PDF
- Proc. Amer. Math. Soc. 136 (2008), 3601-3609 Request permission
Abstract:
In this paper, we introduce a compactification of the moduli space of polynomial maps with a fixed degree $n (\geq 2)$ such that the map from it to $\mathbb {P}^{n-1}(\mathbb {C})$ defined by using the elementary symmetric functions of multipliers at fixed points is a continuous surjection.References
- Lipman Bers, On spaces of Riemann surfaces with nodes, Bull. Amer. Math. Soc. 80 (1974), 1219–1222. MR 361165, DOI 10.1090/S0002-9904-1974-13686-4
- Bodil Branner and John H. Hubbard, The iteration of cubic polynomials. I. The global topology of parameter space, Acta Math. 160 (1988), no. 3-4, 143–206. MR 945011, DOI 10.1007/BF02392275
- Bodil Branner and John H. Hubbard, The iteration of cubic polynomials. II. Patterns and parapatterns, Acta Math. 169 (1992), no. 3-4, 229–325. MR 1194004, DOI 10.1007/BF02392761
- L. DeMarco, Finiteness for degenerate polynomials, arXiv: math/0608800v1.
- L. DeMarco and C. McMullen, Trees and the dynamics of polynomials, arXiv: math/0608759v1.
- Steven P. Diaz, On the Natanzon-Turaev compactification of the Hurwitz space, Proc. Amer. Math. Soc. 130 (2002), no. 3, 613–618. MR 1866008, DOI 10.1090/S0002-9939-01-06393-6
- Steven Diaz and Dan Edidin, Towards the homology of Hurwitz spaces, J. Differential Geom. 43 (1996), no. 1, 66–98. MR 1424420
- Masayo Fujimura, Projective moduli space for the polynomials, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13 (2006), no. 6, 787–801. MR 2273342
- —, The moduli space of rational maps and surjectivity of multiplier representation, Comp. Meth. Funct. Th. 7 (2007), 345–360.
- M. Fujimura and K. Nishizawa, Some dynamical loci of quartic polynomials, J. Japan Soc. Symb. Alg. Compt. 11 (2005), 57–68.
- Y. Imayoshi and M. Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag, Tokyo, 1992. Translated and revised from the Japanese by the authors. MR 1215481, DOI 10.1007/978-4-431-68174-8
- John Milnor, Remarks on iterated cubic maps, Experiment. Math. 1 (1992), no. 1, 5–24. MR 1181083
- Sergei Natanzon and Vladimir Turaev, A compactification of the Hurwitz space, Topology 38 (1999), no. 4, 889–914. MR 1679803, DOI 10.1016/S0040-9383(98)00036-6
- Joseph H. Silverman, The space of rational maps on $\mathbf P^1$, Duke Math. J. 94 (1998), no. 1, 41–77. MR 1635900, DOI 10.1215/S0012-7094-98-09404-2
Additional Information
- Masayo Fujimura
- Affiliation: Department of Mathematics, National Defense Academy, Yokosuka 239-8686, Japan
- Email: masayo@nda.ac.jp
- Masahiko Taniguchi
- Affiliation: Department of Mathematics, Nara Women’s University, Nara 630-8506, Japan
- MR Author ID: 192108
- Email: tanig@cc.nara-wu.ac.jp
- Received by editor(s): June 25, 2007
- Received by editor(s) in revised form: September 3, 2007
- Published electronically: May 8, 2008
- Additional Notes: The second author is partially supported by Grand-in-Aid for Scientific Research 19540181.
- Communicated by: Mei-Chi Shaw
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3601-3609
- MSC (2000): Primary 32G99; Secondary 37F10, 30C15
- DOI: https://doi.org/10.1090/S0002-9939-08-09344-1
- MathSciNet review: 2415044