Indeterminacy Loci of Iterate Maps

Abstract

We consider the indeterminacy locus $I({\Phi }_n)$ of the iterate map ${\Phi }_n:{\overline{M}}_d-rightarrow{\overline{M}}_{d^n}$, 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 $[f]\in I({\Phi }_n)$. These provide partial answers to a question of Laura DeMarco.