Indeterminacy Loci of Iterate Maps
Hongming Nie

TL;DR
This paper investigates the indeterminacy loci of iterate maps in the moduli space of complex rational maps, providing conditions that identify when a map belongs to these loci, thus addressing a question posed by Laura DeMarco.
Contribution
It offers new criteria to determine when a rational map lies in the indeterminacy locus of its iterate map, advancing understanding of the structure of these loci.
Findings
Identifies conditions implying a map is in the indeterminacy locus
Provides partial answers to DeMarco's question
Enhances understanding of iterate map indeterminacy loci
Abstract
We consider the indeterminacy locus of the iterate map , where is the GIT compactification of the moduli space of degree complex rational maps. We give natural conditions on that imply . These provide partial answers to a question of Laura DeMarco.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology
