A portrait on is a pair of finite point sets , a map , and an assignment of weights to the points in . We construct a parameter space whose points correspond to degree endomorphisms such that is as specified by a portrait , and prove the existence of the GIT quotient moduli space under the -action relative to an appropriately chosen line bundle. We also investigate the geometry of and give two arithmetic applications.
"Moduli spaces for dynamical systems with portraits." Illinois J. Math. 64 (3) 375 - 465, September 2020. https://doi.org/10.1215/00192082-8642523