Compactification and trees of spheres covers

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The space of dynamically marked rational maps can be identified with a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In this paper we describe a topology on the quotient of this space under the natural action of its group of isomorphisms. This topology is proved to be consistent with this notion of convergence.

Original languageEnglish
Pages (from-to)225-246
Number of pages22
JournalConformal Geometry and Dynamics
Issue number8
StatePublished - 2017


  • Algebraic geometry
  • Compactification
  • Deligne-Mumford compactification
  • Limits of dynamical systems
  • Noded spheres
  • Rescaling limits
  • Trees of spheres


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