Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2411.08006 |
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Inhaltsangabe:
- Let $χ$ be a (right) action of ${\rm PSL}_{2}({\mathbb L})$ on the space ${\mathbb L}(z)$ of rational maps defined over an algebraically closed field ${\mathbb L}$. If $R \in {\mathbb L}(z)$ and ${\mathcal M}_{R}^χ$ is its $χ$-field of moduli, then the parameter ${\rm FOD/FOM}_χ(R)$ is the smallest integer $n \geq 1$ such that there is a $χ$-field of definition of $R$ being a degree $n$ extension of ${\mathcal M}_{R}^χ$. When ${\mathbb L}$ has characteristic zero and $χ=χ_{\infty}$ is the conjugation action, then it is known that ${\rm FOD/FOM}_{χ_{\infty}}(R) \leq 2$. In this paper, we study the above parameter for general actions and any characteristic.