Compactification and trees of spheres covers

Matthieu Arfeux

doi:10.1090/ecgd/309

Compactification and trees of spheres covers

Matthieu Arfeux

INSTITUTE OF MATHEMATICS

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2 Scopus citations

Abstract

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 language	English
Pages (from-to)	225-246
Number of pages	22
Journal	Conformal Geometry and Dynamics
Volume	21
Issue number	8
DOIs	https://doi.org/10.1090/ecgd/309
State	Published - 2017

Keywords

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

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10.1090/ecgd/309

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title = "Compactification and trees of spheres covers",

abstract = "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.",

keywords = "Algebraic geometry, Compactification, Deligne-Mumford compactification, Limits of dynamical systems, Noded spheres, Rescaling limits, Trees of spheres",

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AB - 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.

KW - Algebraic geometry

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KW - Deligne-Mumford compactification

KW - Limits of dynamical systems

KW - Noded spheres

KW - Rescaling limits

KW - Trees of spheres

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JO - Conformal Geometry and Dynamics

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ER -

Compactification and trees of spheres covers

Abstract

Keywords

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