English

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.

Keywords

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.

R2 v1 2026-06-21T11:18:41.558Z