arXiv subjects
Publications and source records attributed to Hongming Nie.
Suppose $\{f_t\}$ is an analytic one-parameter family of rational maps defined over a non-Archimedean field $K$. We prove a finiteness theorem for the set of rescalings for $\{f_t\}$. This complements results of J. Kiwi.
We consider the indeterminacy locus $I(Φ_n)$ of the iterate map $Φ_n:\overline{M}_d-rightarrow\overline{M}_{d^n}$, where $\overline{M}_d$ is the GIT compactification of the moduli space $M_d$ of degree $d$ complex rational maps. We give natural conditions on $f$ that imply $[f]\in I(Φ_n)$. These provide partial answers to a question of Laura DeMarco.