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arXiv · 1408.3247

The Moduli Space of Cubic Rational Maps

Lloyd W. West
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Abstract

We construct the moduli space, $M_d$, of degree $d$ rational maps on $\mathbb{P}^1$ in terms of invariants of binary forms. We apply this construction to give explicit invariants and equations for $M_3$. Using classical invariant theory, we give solutions to the following problems: (1) explicitly construct, from a moduli point $P\in M_d(k)$, a rational map $\phi$ with the given moduli; (2) find a model for $\phi$ over the field of definition (i.e. explicit descent). We work out the method in detail for the cases $d=2,3$.

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Lloyd W. West. 2014-08-14. The Moduli Space of Cubic Rational Maps. https://arxiv.org/abs/1408.3247

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