Moduli spaces for dynamical systems with portraits
Moduli spaces for dynamical systems with portraits
A $\textit{portrait}$ $\mathcal{P}$ on $\mathbb{P}^N$ is a pair of finite point sets $Y\subseteq{X}\subset\mathbb{P}^N$, a map $Y\to X$, and an assignment of weights to the points in $Y$. We construct a parameter space $\operatorname{End}_d^N[\mathcal{P}]$ whose points correspond to degree $d$ endomorphisms $f:\mathbb{P}^N\to\mathbb{P}^N$ such that $f:Y\to{X}$ is as specified by a portrait …