Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

A compactification of the moduli space of polynomials

Author(s): Masayo Fujimura; Masahiko Taniguchi
Journal: Proc. Amer. Math. Soc. 136 (2008), 3601-3609.
MSC (2000): Primary 32G99; Secondary 37F10, 30C15
Posted: May 8, 2008
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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:

1.
L. Bers, On the space of Riemann surfaces with nodes, Bull. AMS. 80 (1974), 1219-1222. MR 0361165 (50:13611)

2.
B. Branner and J. H. Hubbard, The iteration of cubic polynomials, Part I: The global topology of parameter space, Acta Math. 160 (1988), 143-206. MR 945011 (90d:30073)

3.
-, The iteration of cubic polynomials, Part II: Patterns and parapatterns, Acta Math. 169 (1992), 229-325. MR 1194004 (94d:30044)

4.
L. DeMarco, Finiteness for degenerate polynomials, arXiv: math/0608800v1.

5.
L. DeMarco and C. McMullen, Trees and the dynamics of polynomials, arXiv: math/0608759v1.

6.
S. Diaz, On the Natanzon-Turaev compactification of the Hurwitz space, Proc. AMS 130 (2001), 613-618. MR 1866008 (2002h:14042)

7.
S. Diaz and D. Edidin, Towards the homology of Hurwitz spaces, J. Diff, Geom. 43 (1996), 66-98. MR 1424420 (98e:14028)

8.
M. Fujimura, Projective moduli space for the polynomials, Dynam. Conti. Discrete Impul. Systems 13 (2006), 787-801. MR 2273342 (2007h:37061)

9.
-, The moduli space of rational maps and surjectivity of multiplier representation, Comp. Meth. Funct. Th. 7 (2007), 345-360.

10.
M. Fujimura and K. Nishizawa, Some dynamical loci of quartic polynomials, J. Japan Soc. Symb. Alg. Compt. 11 (2005), 57-68.

11.
Y. Imayoshi and M. Taniguchi, An introduction to Teichmüller spaces, Springer (Tokyo), 1992. MR 1215481 (94b:32031)

12.
J. Milnor, Remarks on iterated cubic maps, Experiment. Math. 1 (1992), 5-24. MR 1181083 (94c:58096)

13.
S. M. Natanzon and V. Turaev, A compactification of the Hurwitz spaces, Topology 38 (1999), 889-914. MR 1679803 (2000b:57004)

14.
J. Silverman, The space of rational maps on $ \mathbb{P}^1$, Duke Math. J. 94 (1998), 41-77. MR 1635900 (2000m:14010)


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32G99, 37F10, 30C15

Retrieve articles in all Journals with MSC (2000): 32G99, 37F10, 30C15


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
Email: tanig@cc.nara-wu.ac.jp

DOI: 10.1090/S0002-9939-08-09344-1
PII: S 0002-9939(08)09344-1
Received by editor(s): June 25, 2007,
Received by editor(s) in revised form: September 3, 2007
Posted: 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 of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google