Moduli spaces for families of rational maps on P^1
Number Theory
2009-02-15 v2 Dynamical Systems
Abstract
Let phi: P^1 --> P^1 be a rational map defined over a field K. We construct the moduli space M_d(N) parameterizing conjugacy classes of degree-d maps with a point of formal period N and present an algebraic proof that M_2(N) is geometrically irreducible for N>1. Restricting ourselves to maps phi of arbitrary degree d >= 2 such that the composition h^{-1} phi h = phi for some nontrivial h in PGL_2, we show that the moduli space parameterizing these maps with a point of formal period N is geometrically reducible for infinitely many N.
Cite
@article{arxiv.0902.1813,
title = {Moduli spaces for families of rational maps on P^1},
author = {Michelle Manes},
journal= {arXiv preprint arXiv:0902.1813},
year = {2009}
}
Comments
48 pages