Holomorphic self-maps of singular rational surfaces
Algebraic Geometry
2010-03-16 v3 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.0809.1724,
title = {Holomorphic self-maps of singular rational surfaces},
author = {Charles Favre},
journal= {arXiv preprint arXiv:0809.1724},
year = {2010}
}
Comments
37 pages. To appear in Publicacions Matematiques.