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arXiv · 2309.15382

The multiplier spectrum morphism is generically injective

Zhuchao Ji·Junyi Xie
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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 Lattès 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.

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Zhuchao Ji, Junyi Xie. 2025-09-22. The multiplier spectrum morphism is generically injective. https://arxiv.org/abs/2309.15382

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