Holomorphic self-maps of singular rational surfaces

Details Holomorphic self-maps of singular rational surfaces Holomorphic self-maps of singular rational surfaces

2008-09-10

arxiv.org/abs/0809.1724v3

Mathematics

Algebraic Geometry

37 pages. To appear in Publicacions Matematiques.

Scientific paper

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.

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