Computational Methods and Function Theory

, Volume 7, Issue 2, pp 345–360 | Cite as

The Moduli Space of Rational Maps and Surjectivity of Multiplier Representation

Article

Abstract

In this paper, we first show that the map ΨRat n of the moduli space of rational maps of degree n to ℂn obtained from multipliers at fixed points is always surjective, while the map ΨPoly n of the moduli space of polynomials of degree n to ℂ nt 1 defined similarly is never so if n ≥ 4. Next, in the latter case, we give a sufficient condition and a necessary one for points not in the image of ΨPoly n, and give an explicit parametrization for all such points if n = 4 or 5. Also, we show that the preimage of a generic point by ΨPoly n consists of (n − 2)! points.

Keywords

Rational maps fixed points multiplier moduli space 

2000 MSC

30C10 37C25 

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Copyright information

© Heldermann  Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsNational Defense AcademyYokosukaJapan

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