Holomorphic self-maps of singular rational surfaces

We give a new proof of the classification of normal singular surface germs admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw an analogy between the birational classification of singular holomorphic foliations on surfaces, and the dynamics of holomorphic maps. Following...

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Detalles Bibliográficos
Autor: Favre, Charles
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:57596
Acceso en línea:https://ddd.uab.cat/record/57596
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_54210_06
Access Level:acceso abierto
Palabra clave:Rational maps
Dynamics
Surface singularity
Valuation space
Descripción
Sumario:We give a new proof of the classification of normal singular surface germs admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw an analogy between the birational classification of singular holomorphic foliations on surfaces, and the dynamics of holomorphic maps. Following this analogy, we introduce the notion of minimal holomorphic model for holomorphic maps. We give sufficient conditions which ensure the uniqueness of such a model.