The multiplier spectrum morphism is generically injective
Dynamical Systems
2025-09-23 v3 Algebraic Geometry
Abstract
In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated theorem of McMullen asserts that aside from the well-understood flexible Latt\`es family, the multiplier spectrum morphism is quasi-finite. In this paper, we strengthen McMullen's theorem by showing that the multiplier spectrum morphism is generically injective. This answers a question of McMullen and Poonen.
Keywords
Cite
@article{arxiv.2309.15382,
title = {The multiplier spectrum morphism is generically injective},
author = {Zhuchao Ji and Junyi Xie},
journal= {arXiv preprint arXiv:2309.15382},
year = {2025}
}
Comments
J. Eur. Math. Soc, to appear