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.