Stratification and coordinate systems for the moduli space of rational functions
Masayo Fujimura, Masahiko Taniguchi
TL;DR
This paper introduces a new global parameter system for the moduli space of rational functions, clarifies its relation to fixed point parameters, and confirms a conjecture by Milnor.
Contribution
It provides a simplified global parameterization of the moduli space and resolves Milnor's conjecture.
Findings
Established a new simple global parameter system
Clarified the relation to fixed point locations and indices
Confirmed Milnor's conjecture
Abstract
In this note, we give a new simple system of global parameters on the moduli space of rational functions, and clarify the relation to the parameters indicating location of fixed points and the indices at them. As a byproduct, we solve a conjecture of Milnor affirmatively.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation